Calculating Distance

24 questions

Question 1Question →

A transport aircraft flies at a constant cruising speed of 360 miles per hour360\text{ miles per hour}. If it maintains this speed, what is the total distance it travels in 40 minutes40\text{ minutes}, in miles?

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Answer: 240

Answer

240
To find the distance, the time must first be converted to match the 'hours' unit in the speed rate. Forty minutes is equal to two-thirds of an hour. Multiplying the rate of 360 miles per hour360\text{ miles per hour} by 23 of an hour\frac{2}{3}\text{ of an hour} yields a total distance of 240 miles240\text{ miles}.

Step-by-Step Solution

1
Convert the travel time from minutes to hours.
23 hours\frac{2}{3}\text{ hours}
The speed is given in miles per hour, so the time must be converted to hours to ensure the units cancel out correctly during multiplication.
2
Calculate the distance using the formula Distance=Rate×TimeDistance = Rate \times Time.
240 miles240\text{ miles}
Multiplying the constant rate of 360 mph360\text{ mph} by the travel time of 23 hours\frac{2}{3}\text{ hours} yields the total distance traveled.

Key Concept

Calculating distance using a constant rate and performing a basic time unit conversion.

Alternative Method

You can also find the distance traveled per minute by dividing 360 miles360\text{ miles} by 60 minutes60\text{ minutes}, which equals 6 miles per minute6\text{ miles per minute}. Then, multiply 6 miles per minute6\text{ miles per minute} by 40 minutes40\text{ minutes} to get 240 miles240\text{ miles}.
Estimated Time:45s
Question 2Question →

A specialized reconnaissance team hikes through rough terrain at a steady pace of 3 mph3\text{ mph} for 1 hour and 40 minutes1\text{ hour and } 40\text{ minutes}. They then rendezvous with an extraction helicopter that flies them to a base at an average speed of 150 mph150\text{ mph} for 24 minutes24\text{ minutes}. What is the total distance covered by the team? (Provide your answer in miles, e.g., '50 miles')

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Answer: 65 miles; 65; 65 mi; 65mi; 65.0 miles; sixty-five miles

Answer

65 miles
The correct answer is found by calculating the distance of each leg separately using the formula Distance = Rate × Time, ensuring all times are properly converted into hours, and then summing the two distances (5 miles + 60 miles = 65 miles).

Step-by-Step Solution

1
Convert the hiking time into hours.
1 hour and 40 minutes = 1 + 40/60 hours = 5/3 hours.
Speed is given in miles per hour, so time must be in hours to properly use the distance formula.
2
Calculate the distance covered during the hike.
Distance = Rate × Time = 3 mph × (5/3) hours = 5 miles.
This finds the length of the first leg of the journey.
3
Convert the helicopter flight time into hours.
24 minutes = 24/60 hours = 2/5 hours (or 0.4 hours).
Again, the helicopter speed is in mph, requiring time to be in hours.
4
Calculate the distance covered by the helicopter.
Distance = Rate × Time = 150 mph × 0.4 hours = 60 miles.
This finds the length of the second leg of the journey.
5
Calculate the total distance covered.
5 miles + 60 miles = 65 miles.
The total distance is the sum of the individual leg distances.

Key Concept

Calculating distance for multiple legs of a journey with mixed time units.
Question 3Question →

A patrol unit drives at a steady speed of 20 mph20\text{ mph} for 33 hours along a desert trail. They then enter a paved highway and drive at 50 mph50\text{ mph} for 22 hours. What is the total distance traveled by the patrol unit?

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Answer: 160; 160 miles; 160 mi; 160miles; 160.0

Answer

160 miles
To find the total distance, you must calculate the distance for each part of the journey separately. For the first leg, the distance is 20 mph×3 hours=60 miles20\text{ mph} \times 3\text{ hours} = 60\text{ miles}. For the second leg, the distance is 50 mph×2 hours=100 miles50\text{ mph} \times 2\text{ hours} = 100\text{ miles}. Adding these two distances together (60+10060 + 100) gives a total distance of 160160 miles.

Step-by-Step Solution

1
Calculate the distance traveled during the first segment on the desert trail.
Distance = Rate × Time = 20 mph × 3 hours = 60 miles
The distance formula D=R×TD = R \times T is used to find the distance for each constant-speed leg of the trip.
2
Calculate the distance traveled during the second segment on the paved highway.
Distance = Rate × Time = 50 mph × 2 hours = 100 miles
Applying the same formula to the second leg provides the remaining distance.
3
Add the distances from both segments to find the total distance traveled.
60 miles + 100 miles = 160 miles
The total distance of a multi-leg journey is the sum of the distances of each individual segment.

Key Concept

Calculating total distance for a multi-leg journey using the formula Distance = Rate × Time (D=R×TD = R \times T).
Question 4Question →

A military supply truck travels at a steady rate of 40 mph40\text{ mph} for exactly 4545 minutes along a designated supply route. What is the total distance traveled?

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Answer: 30 miles30\text{ miles}

Answer

30 miles30\text{ miles}
To find the correct distance, the time must first be converted to match the units of the rate. Dividing 45 minutes45\text{ minutes} by 6060 gives 0.75 hours0.75\text{ hours}. Multiplying the rate (40 mph40\text{ mph}) by the time (0.75 hours0.75\text{ hours}) gives exactly 30 miles30\text{ miles}.

Step-by-Step Solution

1
Convert the travel time from minutes to hours.
45 minutes=4560 hours=0.75 hours45\text{ minutes} = \frac{45}{60}\text{ hours} = 0.75\text{ hours}
The speed is given in miles per hour (mph), so the time must be in hours to cancel out the units properly.
2
Calculate the total distance using the formula: Distance = Rate ×\times Time.
Distance =40 mph×0.75 hours=30 miles= 40\text{ mph} \times 0.75\text{ hours} = 30\text{ miles}
Multiplying the steady rate by the total time in hours yields the total distance.

Key Concept

Calculating Distance with Unit Conversion
Question 5Question →

A naval submarine travels at a steady surface speed of 15 knots15\text{ knots} (nautical miles per hour) for 2 hours and 20 minutes2\text{ hours and } 20\text{ minutes} before submerging. What is the total distance traveled during this time?

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Answer: 35 nautical miles35\text{ nautical miles}

Answer

35 nautical miles35\text{ nautical miles}
The correct answer is found by converting the travel time of 2 hours and 20 minutes2\text{ hours and } 20\text{ minutes} into 213 hours2\frac{1}{3}\text{ hours}, and then multiplying this time by the speed of 15 knots15\text{ knots}. The calculation is 15×73=35 nautical miles15 \times \frac{7}{3} = 35\text{ nautical miles}.

Step-by-Step Solution

1
Convert the travel time into hours.
2 hours and 20 minutes=22060 hours=213 hours2\text{ hours and } 20\text{ minutes} = 2\frac{20}{60}\text{ hours} = 2\frac{1}{3}\text{ hours}.
Speed is given in knots (nautical miles per hour), so time must be uniformly converted to hours to compute distance accurately.
2
Multiply the speed by the time to find the total distance.
Distance=15×213=15×73=35 nautical miles\text{Distance} = 15 \times 2\frac{1}{3} = 15 \times \frac{7}{3} = 35\text{ nautical miles}.
The formula for distance is Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}.

Key Concept

Calculating distance by converting minutes into a fraction of an hour and multiplying by the rate of speed.
Question 6Question →

A coastal patrol boat is conducting a surveillance mission. It travels at a steady speed of 12 knots12\text{ knots} (nautical miles per hour) for 2 hours2\text{ hours} and 15 minutes15\text{ minutes}. It then increases its speed to 20 knots20\text{ knots} for 12 minutes12\text{ minutes} to intercept a vessel. What is the total distance traveled by the patrol boat, in nautical miles?

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Answer: 3131

Answer

The correct answer is 3131 nautical miles.
The total distance is found by calculating the distance for each leg separately. First, convert the times into hours: 15 minutes15\text{ minutes} is 0.25 hours0.25\text{ hours} (making the first leg 2.25 hours2.25\text{ hours}), and 12 minutes12\text{ minutes} is 0.2 hours0.2\text{ hours}. Multiplying these times by their respective speeds (12×2.2512 \times 2.25 and 20×0.220 \times 0.2) gives distances of 2727 and 44 nautical miles. Adding these together yields a total of 3131 nautical miles.

Step-by-Step Solution

1
Convert the time of the first leg into hours.
2 hours and 15 minutes=2+1560=2.25 hours2\text{ hours and } 15\text{ minutes} = 2 + \frac{15}{60} = 2.25\text{ hours}.
Speed is given in knots (nautical miles per hour), so the time must be in hours to cancel the units properly.
2
Calculate the distance traveled during the first leg.
12 knots×2.25 hours=27 nautical miles12\text{ knots} \times 2.25\text{ hours} = 27\text{ nautical miles}.
Using the formula Distance = Rate x Time.
3
Convert the time of the second leg into hours.
12 minutes=1260=0.2 hours12\text{ minutes} = \frac{12}{60} = 0.2\text{ hours}.
Maintaining consistent units across all calculations.
4
Calculate the distance traveled during the second leg.
20 knots×0.2 hours=4 nautical miles20\text{ knots} \times 0.2\text{ hours} = 4\text{ nautical miles}.
Using the formula Distance = Rate x Time for the second segment.
5
Add the distances of both legs to find the total distance.
27+4=31 nautical miles27 + 4 = 31\text{ nautical miles}.
The total distance is the sum of the individual segments of the journey.

Key Concept

Calculating total distance for multi-leg journeys requires converting mixed time units into hours and applying the Distance = Rate x Time formula to each leg separately.
Question 7Question →

During a morning commute, a passenger train maintains a constant speed of 48 miles per hour48\text{ miles per hour} between two city stations. If the non-stop journey takes exactly 1515 minutes, what is the total distance between the two stations?

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Answer: 12 miles12\text{ miles}

Answer

The distance between the two stations is 12 miles12\text{ miles}.
The correct answer is found by first converting 1515 minutes to hours by dividing by 6060, which gives 0.250.25 hours. Then, multiplying the speed of 48 miles per hour48\text{ miles per hour} by 0.250.25 hours results in a distance of 12 miles12\text{ miles}.

Step-by-Step Solution

1
Identify the formula for distance.
Distance=Rate×TimeDistance = Rate \times Time
This formula connects speed, time, and distance to find the unknown value.
2
Convert the travel time from minutes to hours.
15 minutes=1560 hours=0.25 hours15 \text{ minutes} = \frac{15}{60} \text{ hours} = 0.25 \text{ hours}
The rate is given in miles per hour, so the time must be in hours to cancel out the units correctly.
3
Multiply the rate by the converted time.
48×0.25=1248 \times 0.25 = 12
Applying the values to the distance formula yields the total distance in miles.

Key Concept

Calculating distance by converting time units to match the rate units.
Estimated Time:45s
Question 8Question →

A freight train departs from a central hub to deliver materials across two different transit zones. In the primary zone, the train maintains a constant speed of 60 mph60\text{ mph} for 2 hours and 45 minutes2\text{ hours and } 45\text{ minutes}. Upon entering the secondary zone, it reduces its speed to 40 mph40\text{ mph} for the remaining 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes} of the route. What is the total distance traveled by the freight train?

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Answer: 215 miles215\text{ miles}

Answer

The freight train traveled a total distance of 215 miles215\text{ miles}.
To find the total distance, each segment must be calculated separately using the formula Distance=Speed×Time\text{Distance} = \text{Speed} \times \text{Time}. For the primary zone, 2 hours and 45 minutes2\text{ hours and } 45\text{ minutes} is 2.75 hours2.75\text{ hours}. Multiplying 60 mph60\text{ mph} by 2.75 hours2.75\text{ hours} yields 165 miles165\text{ miles}. For the secondary zone, 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes} is 1.25 hours1.25\text{ hours}. Multiplying 40 mph40\text{ mph} by 1.25 hours1.25\text{ hours} yields 50 miles50\text{ miles}. The total distance is the sum of these two segments: 165+50=215 miles165 + 50 = 215\text{ miles}.

Step-by-Step Solution

1
Convert the travel time for the primary zone into hours.
2 hours and 45 minutes=2+4560=2.75 hours2\text{ hours and } 45\text{ minutes} = 2 + \frac{45}{60} = 2.75\text{ hours}.
Speed is given in miles per hour (mph), so time must be in hours to calculate distance.
2
Calculate the distance traveled in the primary zone.
Distance=Speed×Time=60 mph×2.75 hours=165 miles\text{Distance} = \text{Speed} \times \text{Time} = 60\text{ mph} \times 2.75\text{ hours} = 165\text{ miles}.
Applying the standard distance formula for the first segment.
3
Convert the travel time for the secondary zone into hours.
1 hour and 15 minutes=1+1560=1.25 hours1\text{ hour and } 15\text{ minutes} = 1 + \frac{15}{60} = 1.25\text{ hours}.
Time must be consistently in hours to match the speed unit.
4
Calculate the distance traveled in the secondary zone.
Distance=40 mph×1.25 hours=50 miles\text{Distance} = 40\text{ mph} \times 1.25\text{ hours} = 50\text{ miles}.
Applying the distance formula for the second segment.
5
Add the distances of both zones to find the total distance.
165 miles+50 miles=215 miles165\text{ miles} + 50\text{ miles} = 215\text{ miles}.
The total distance is the sum of all individual legs of the journey.

Key Concept

Calculating distance across multiple segments requires converting time into consistent units (hours) before applying the distance formula (d=rtd = rt) to each segment and summing the results.
Question 9Question →

A military supply convoy travels at a steady speed of 40 miles per hour40\text{ miles per hour} for 2 hours2\text{ hours}. Then, it travels at a steady speed of 50 miles per hour50\text{ miles per hour} for 1 hour1\text{ hour}. What is the total distance traveled by the convoy? Provide your answer including the unit (e.g., '130 miles').

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Answer: 130 miles; 130 mi; 130

Answer

130 miles
To find the total distance, you must calculate the distance for each segment separately using the formula Distance = Rate × Time, and then add them together. The first segment covers 80 miles (40 mph × 2 hours) and the second segment covers 50 miles (50 mph × 1 hour), resulting in a total distance of 130 miles.

Step-by-Step Solution

1
Calculate the distance for the first part of the trip.
40×2=80 miles40 \times 2 = 80\text{ miles}
Distance is equal to rate multiplied by time.
2
Calculate the distance for the second part of the trip.
50×1=50 miles50 \times 1 = 50\text{ miles}
Apply the distance formula to the second segment.
3
Add the distances from both parts of the trip to find the total distance.
80+50=130 miles80 + 50 = 130\text{ miles}
The total distance is the sum of the individual segment distances.

Key Concept

Calculating total distance for a multi-segment journey by applying the formula Distance = Rate × Time to each segment.
Estimated Time:45s
Question 10Question →

A logistical transport convoy travels along a main supply route at a steady speed of 55 miles per hour55\text{ miles per hour}. If the journey takes exactly 3 hours and 36 minutes3\text{ hours and } 36\text{ minutes}, what is the total distance traveled in miles?

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Answer: 198

Answer

The convoy traveled a total distance of 198 miles.
The correct total distance is determined by first converting the mixed travel time entirely into hours (3.6 hours3.6\text{ hours}) and then multiplying it by the constant speed (55 mph55\text{ mph}) to yield exactly 198 miles198\text{ miles}.

Step-by-Step Solution

1
Convert the travel time into a single unit (hours) to match the rate.
3 hours and 36 minutes=3+3660 hours=3.6 hours3\text{ hours and } 36\text{ minutes} = 3 + \frac{36}{60}\text{ hours} = 3.6\text{ hours}.
The speed is given in miles per hour, so the time must be represented entirely in hours before multiplying.
2
Apply the distance formula: Distance = Rate ×\times Time.
Distance = 55×3.655 \times 3.6
This formula determines the total distance covered over a specific time frame at a constant speed.
3
Calculate the final distance.
198198
Multiplying the constant rate of 55 mph55\text{ mph} by the total duration of 3.6 hours3.6\text{ hours} yields the total miles traveled.

Key Concept

Calculating distance using a constant rate and converting mixed time units.
Question 11Question →

A coast guard rescue helicopter flies directly toward a distressed vessel at a constant speed of 120 miles per hour120\text{ miles per hour}. If the flight takes exactly 45 minutes45\text{ minutes}, what is the total distance traveled by the helicopter?

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Answer: 90 miles90\text{ miles}

Answer

The total distance traveled by the helicopter is 90 miles90\text{ miles}.
The correct answer accurately converts the 45 minutes45\text{ minutes} of flight time into 0.75 hours0.75\text{ hours}, and then applies the distance formula (D=R×TD = R \times T) to find 120×0.75=90 miles120 \times 0.75 = 90\text{ miles}.

Step-by-Step Solution

1
Convert the flight time from minutes to hours.
45 minutes=4560 hours=0.75 hours45\text{ minutes} = \frac{45}{60}\text{ hours} = 0.75\text{ hours}.
The speed is given in miles per hour, so the time must also be in hours to calculate the distance correctly.
2
Calculate the distance using the formula Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}.
120 miles per hour×0.75 hours=90 miles120\text{ miles per hour} \times 0.75\text{ hours} = 90\text{ miles}.
Multiplying the constant speed by the total time in hours gives the total distance traveled.

Key Concept

To find distance, multiply the rate of speed by the time traveled, ensuring that the units of time match the units in the speed rate.
Question 12Question →

A Coast Guard search and rescue helicopter departs its base and flies toward a distress signal at a steady speed of 140 knots140\text{ knots} for 45 minutes45\text{ minutes}. Upon arriving at the scene, the helicopter hovers in place for 15 minutes15\text{ minutes} to hoist a survivor. It then flies directly to a coastal hospital at a steady speed of 160 knots160\text{ knots}, arriving after 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes}. What is the total distance traveled by the helicopter during this mission?

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Answer: 305 nautical miles305\text{ nautical miles}

Answer

305 nautical miles305\text{ nautical miles}
The correct answer is found by determining the distance of each flight leg separately and adding them together. First, convert the times into hours: 45 minutes45\text{ minutes} is 0.75 hours0.75\text{ hours}, and 1 hour 15 minutes1\text{ hour } 15\text{ minutes} is 1.25 hours1.25\text{ hours}. Then, apply the formula Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}. The first leg is 140 knots×0.75 hours=105 nautical miles140\text{ knots} \times 0.75\text{ hours} = 105\text{ nautical miles}. The hover adds 00 distance. The final leg is 160 knots×1.25 hours=200 nautical miles160\text{ knots} \times 1.25\text{ hours} = 200\text{ nautical miles}. Adding these segments together (105+200105 + 200) yields a total distance of 305 nautical miles305\text{ nautical miles}.

Step-by-Step Solution

1
Convert the travel time of the first leg from minutes to hours.
45 minutes=45/60=0.75 hours45\text{ minutes} = 45 / 60 = 0.75\text{ hours}
Speed is given in knots (nautical miles per hour), so the time must be represented in hours.
2
Calculate the distance traveled during the first leg.
140 knots×0.75 hours=105 nautical miles140\text{ knots} \times 0.75\text{ hours} = 105\text{ nautical miles}
Distance is equal to rate multiplied by time.
3
Determine the distance traveled during the hover phase.
0 nautical miles0\text{ nautical miles}
The helicopter is stationary while hovering, so no distance is covered.
4
Convert the travel time of the final leg to hours.
1 hour and 15 minutes=1+(15/60)=1.25 hours1\text{ hour and } 15\text{ minutes} = 1 + (15 / 60) = 1.25\text{ hours}
Consistent units are required to accurately apply the distance formula.
5
Calculate the distance traveled during the final leg.
160 knots×1.25 hours=200 nautical miles160\text{ knots} \times 1.25\text{ hours} = 200\text{ nautical miles}
Using the distance formula again for the final phase of the journey.
6
Sum the distances from all phases of the mission.
105+0+200=305 nautical miles105 + 0 + 200 = 305\text{ nautical miles}
The total mission distance is the sum of the distances covered in each individual segment.

Key Concept

Calculating distance across multiple segments by converting time to consistent units and applying the Distance = Rate × Time formula for each segment.
Question 13Question →

An armored reconnaissance vehicle is conducting a route clearance mission. It travels at a steady speed of 32 miles per hour32\text{ miles per hour} for 45 minutes45\text{ minutes}. Then, due to rough terrain, its speed drops to 16 miles per hour16\text{ miles per hour} for the next 1 hour1\text{ hour} and 15 minutes15\text{ minutes}. What is the total distance the vehicle traveled, in miles?

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Answer: 44; 44 miles; 44 mi; forty-four; 44.0

Answer

44 miles
To find the total distance traveled, we evaluate each leg of the trip using the formula Distance = Rate × Time. The first leg is driven at 32 mph for 45 minutes (which is 0.75 hours). Distance = 32 × 0.75 = 24 miles. The second leg is driven at 16 mph for 1 hour and 15 minutes (which is 1.25 hours). Distance = 16 × 1.25 = 20 miles. The total distance is the sum of these two segments: 24 + 20 = 44 miles.

Step-by-Step Solution

1
Convert the travel time of the first leg from minutes to hours.
45 minutes=4560 hours=0.75 hours45\text{ minutes} = \frac{45}{60}\text{ hours} = 0.75\text{ hours}
The speed is given in miles per hour, so the time must be in hours to calculate the distance properly.
2
Calculate the distance covered during the first leg.
32 mph×0.75 hours=24 miles32\text{ mph} \times 0.75\text{ hours} = 24\text{ miles}
Using the formula Distance = Rate × Time.
3
Convert the travel time of the second leg to hours.
1 hour1\text{ hour} and 15 minutes=1+1560 hours=1.25 hours15\text{ minutes} = 1 + \frac{15}{60}\text{ hours} = 1.25\text{ hours}
Time must be consistently in hours to match the rate of 16 mph.
4
Calculate the distance covered during the second leg.
16 mph×1.25 hours=20 miles16\text{ mph} \times 1.25\text{ hours} = 20\text{ miles}
Using the formula Distance = Rate × Time.
5
Add the distances of both legs to find the total distance.
24 miles+20 miles=44 miles24\text{ miles} + 20\text{ miles} = 44\text{ miles}
The total distance is the sum of the individual segments.

Key Concept

Calculating distance across multiple journey segments requiring time unit conversions.
Question 14Question →

A naval destroyer is tasked with an interception mission. It travels in a straight line at a constant speed of 35 knots35\text{ knots} (where 1 knot=1 nautical mile per hour1\text{ knot} = 1\text{ nautical mile per hour}) for exactly 3 hours and 12 minutes3\text{ hours and } 12\text{ minutes}. What is the total distance traveled by the destroyer?

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Answer: 112 nautical miles112\text{ nautical miles}

Answer

112 nautical miles112\text{ nautical miles}
The correct distance is found by converting the travel time entirely into hours to match the rate. Since there are 60 minutes in an hour, 12 minutes12\text{ minutes} is equal to 0.2 hours0.2\text{ hours} (12÷6012 \div 60). Adding this to the 3 hours gives a total travel time of 3.2 hours3.2\text{ hours}. Multiplying the rate of 35 knots35\text{ knots} by 3.2 hours3.2\text{ hours} yields exactly 112 nautical miles112\text{ nautical miles}.

Step-by-Step Solution

1
Convert the given time into a single unit that matches the rate (hours).
12 minutes÷60 minutes/hour=0.2 hours12\text{ minutes} \div 60\text{ minutes/hour} = 0.2\text{ hours}. Total time = 3.2 hours3.2\text{ hours}.
Speed is given in knots (nautical miles per hour), so time must be expressed purely in hours to use the formula Distance = Rate x Time.
2
Multiply the rate of speed by the total time in hours.
35 knots×3.2 hours=112 nautical miles35\text{ knots} \times 3.2\text{ hours} = 112\text{ nautical miles}.
Applying the distance formula (d = r * t) yields the total distance traveled.

Key Concept

Calculating distance by converting mixed time units into a decimal fraction of an hour before multiplying by speed.
Question 15Question →

A dispatch rider is transporting urgent documents between two military installations. The rider travels on a paved highway at a constant speed of 65 mph65\text{ mph} for 1 hour and 12 minutes1\text{ hour and } 12\text{ minutes}. Upon reaching a rural sector, the rider continues on an unpaved route at a steady speed of 42 mph42\text{ mph} for 35 minutes35\text{ minutes}. What is the total distance, in miles, the dispatch rider traveled?

Show answer & explanation

Answer: 102.5

Answer

102.5
To find the total distance, calculate the distance for each leg of the trip separately by ensuring time is expressed in hours. For the first leg, 1 hour and 12 minutes1\text{ hour and } 12\text{ minutes} is 1.2 hours1.2\text{ hours}. Multiplying the 65 mph65\text{ mph} rate by 1.2 hours1.2\text{ hours} gives 78 miles78\text{ miles}. For the second leg, 35 minutes35\text{ minutes} is 3560\frac{35}{60} or 712 of an hour\frac{7}{12}\text{ of an hour}. Multiplying the 42 mph42\text{ mph} rate by 712 hours\frac{7}{12}\text{ hours} gives 24.5 miles24.5\text{ miles}. Adding these two distances together (78+24.578 + 24.5) gives a total of 102.5 miles102.5\text{ miles}.

Step-by-Step Solution

1
Convert the highway travel time into hours.
1 hour and 12 minutes=1+1260 hours=1.2 hours1\text{ hour and } 12\text{ minutes} = 1 + \frac{12}{60}\text{ hours} = 1.2\text{ hours}.
The speed is given in miles per hour, so time must be converted to hours to match units.
2
Calculate the distance traveled on the highway.
65 mph×1.2 hours=78 miles65\text{ mph} \times 1.2\text{ hours} = 78\text{ miles}.
Applying the formula: Distance = Rate ×\times Time.
3
Convert the unpaved route travel time into hours.
35 minutes=3560 hours=712 hours35\text{ minutes} = \frac{35}{60}\text{ hours} = \frac{7}{12}\text{ hours}.
Time must be in hours for consistency with the speed unit.
4
Calculate the distance traveled on the unpaved route.
42 mph×712 hours=24.5 miles42\text{ mph} \times \frac{7}{12}\text{ hours} = 24.5\text{ miles}.
Applying the formula: Distance = Rate ×\times Time.
5
Calculate the total distance.
78 miles+24.5 miles=102.5 miles78\text{ miles} + 24.5\text{ miles} = 102.5\text{ miles}.
The total journey distance is the sum of the individual distances from each leg.

Key Concept

Calculating total distance for a multi-leg journey by accurately converting fractional times to hours and applying the distance formula.
Question 16Question →

A disaster relief team is transporting supplies to a stricken area. They first drive their trucks on a paved highway at a constant speed of 52 miles per hour52\text{ miles per hour} for 1 hour and 15 minutes1\text{ hour and } 15\text{ minutes}. They then transition to rough off-road terrain, where they travel at a steady speed of 18 miles per hour18\text{ miles per hour} for 40 minutes40\text{ minutes} to reach their final destination. What is the total distance traveled by the team?

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Answer: 77 miles77\text{ miles}

Answer

The correct total distance is 77 miles77\text{ miles}.
The total distance is the sum of the distances from both legs of the trip. The first leg is 1 hour and 15 minutes (1.25 hours) at 52 mph, which equals 65 miles. The second leg is 40 minutes (2/3 of an hour) at 18 mph, which equals 12 miles. Adding these gives a total of 77 miles.

Step-by-Step Solution

1
Convert the travel time for the first leg into hours.
1 hour and 15 minutes=11560 hours=1.25 hours1\text{ hour and } 15\text{ minutes} = 1\frac{15}{60}\text{ hours} = 1.25\text{ hours}.
Speed is given in miles per hour, so time must be converted into hours to correctly calculate the distance.
2
Calculate the distance traveled during the first leg.
52 mph×1.25 hours=65 miles52\text{ mph} \times 1.25\text{ hours} = 65\text{ miles}.
Distance equals rate multiplied by time (D=R×TD = R \times T).
3
Convert the travel time for the second leg into hours.
40 minutes=4060 hours=23 hours40\text{ minutes} = \frac{40}{60}\text{ hours} = \frac{2}{3}\text{ hours}.
Consistent units are required for the second leg's calculation.
4
Calculate the distance traveled during the second leg.
18 mph×23 hours=12 miles18\text{ mph} \times \frac{2}{3}\text{ hours} = 12\text{ miles}.
Using the D=R×TD = R \times T formula for the off-road section.
5
Add the distances of both legs to find the total distance.
65 miles+12 miles=77 miles65\text{ miles} + 12\text{ miles} = 77\text{ miles}.
The question asks for the total combined distance traveled by the team to reach their destination.

Key Concept

Calculating total distance for multi-leg journeys by applying the D=R×TD = R \times T formula with necessary time unit conversions.
Estimated Time:1m 30s
Question 17Question →

A naval submarine travels completely submerged at a steady cruising speed of 40 knots40\text{ knots}. If it maintains this speed for 3 hours and 15 minutes3\text{ hours and } 15\text{ minutes} during a continuous sonar patrol, what is the total distance covered?

Show answer & explanation

Answer: 130 nautical miles130\text{ nautical miles}

Answer

130 nautical miles130\text{ nautical miles}
The correct answer is derived by converting the 15 minutes15\text{ minutes} into 0.25 hours0.25\text{ hours}, yielding a total continuous travel time of 3.25 hours3.25\text{ hours}. Multiplying the cruising speed of 40 knots40\text{ knots} by 3.25 hours3.25\text{ hours} results in exactly 130 nautical miles130\text{ nautical miles}.

Step-by-Step Solution

1
Identify the standard distance formula.
Distance=Rate×Time\text{Distance} = \text{Rate} \times \text{Time}
This formula connects speed, travel time, and distance covered.
2
Convert the mixed time measurement (3 hours and 15 minutes3\text{ hours and } 15\text{ minutes}) entirely into hours.
15 minutes÷60 minutes/hour=0.25 hours15\text{ minutes} \div 60\text{ minutes/hour} = 0.25\text{ hours}. Total time is 3+0.25=3.25 hours3 + 0.25 = 3.25\text{ hours}.
The rate is given in knots (nautical miles per hour), so the time must be strictly in hours before multiplication.
3
Multiply the rate by the total time in hours.
40×3.25=130 nautical miles40 \times 3.25 = 130\text{ nautical miles}
Applying the values to the distance formula yields the total traveled distance.

Key Concept

Calculating distance by standardizing mixed time units (hours and minutes) into a single metric before multiplying by rate.
Question 18Question →

A military cargo plane flies from Base Alpha to Base Bravo at a steady cruising speed of 320 miles per hour320\text{ miles per hour}. This first leg of the flight takes 2 hours and 45 minutes2\text{ hours and } 45\text{ minutes}. After refueling, the plane continues to Base Charlie, flying at 280 miles per hour280\text{ miles per hour} for 1 hour and 30 minutes1\text{ hour and } 30\text{ minutes}. What is the total distance traveled by the cargo plane from Base Alpha to Base Charlie? Include both the numeric value and unit in your answer (e.g., '500 miles').

Show answer & explanation

Answer: 1300 miles; 1,300 miles; 1300 mi; 1300; 1,300

Answer

1300 miles
The correct answer is found by first converting all travel times into decimal hours. The first leg is 2.752.75 hours at 320 mph320\text{ mph}, covering 880 miles880\text{ miles}. The second leg is 1.51.5 hours at 280 mph280\text{ mph}, covering 420 miles420\text{ miles}. Adding these two distances yields a total of 1300 miles1300\text{ miles}.

Step-by-Step Solution

1
Convert the flight times into decimal hours.
2 hours and 45 minutes=2.75 hours2\text{ hours and } 45\text{ minutes} = 2.75\text{ hours}; 1 hour and 30 minutes=1.5 hours1\text{ hour and } 30\text{ minutes} = 1.5\text{ hours}.
To calculate distance using miles per hour, the time units must be converted to hours.
2
Calculate the distance for the first leg from Base Alpha to Base Bravo.
320 mph×2.75 hours=880 miles320\text{ mph} \times 2.75\text{ hours} = 880\text{ miles}.
Distance equals rate multiplied by time (d=r×td = r \times t).
3
Calculate the distance for the second leg from Base Bravo to Base Charlie.
280 mph×1.5 hours=420 miles280\text{ mph} \times 1.5\text{ hours} = 420\text{ miles}.
The second leg must be calculated independently due to the change in both speed and travel time.
4
Add the distances of both legs to find the total distance traveled.
880 miles+420 miles=1300 miles880\text{ miles} + 420\text{ miles} = 1300\text{ miles}.
The total journey distance is the sum of the distances of all individual legs.

Key Concept

Calculating multi-leg total distance using d=r×td = r \times t with unit conversions.
Question 19Question →

An armored convoy travels from Camp Alpha to Camp Bravo. For the first segment of the trip, the convoy travels at an average speed of 45 mph for 1 hour and 20 minutes. They then stop for a 45-minute rest. After the rest, the convoy resumes travel at an average speed of 30 mph for 2 hours and 15 minutes to reach Camp Bravo. Upon arrival, the convoy immediately takes a different, more direct route back to Camp Alpha. The return route is 20% shorter than the total distance they traveled to reach Camp Bravo. What is the total distance the convoy traveled during the entire round trip?

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Answer: 229.5 miles

Answer

229.5 miles
The correct answer accurately synthesizes multiple principles: converting mixed time units into exact hourly fractions, calculating distance for separate legs using D=RTD = RT, applying a percent reduction to find a new distance, and summing all legs to find the aggregate total distance of a round trip.

Step-by-Step Solution

1
Calculate the distance covered during the first travel segment.
6060 miles
Convert 1 hour 20 minutes into hours: 1+2060=1+13=431 + \frac{20}{60} = 1 + \frac{1}{3} = \frac{4}{3} hours. Multiply by speed: 45×43=6045 \times \frac{4}{3} = 60 miles.
2
Calculate the distance covered during the second travel segment.
67.567.5 miles
Convert 2 hours 15 minutes into hours: 2+1560=2+14=2.252 + \frac{15}{60} = 2 + \frac{1}{4} = 2.25 hours. Multiply by speed: 30×2.25=67.530 \times 2.25 = 67.5 miles. (The 45-minute rest adds 0 distance).
3
Find the total outbound distance to Camp Bravo.
127.5127.5 miles
Add the distances from the first and second segments: 60+67.5=127.560 + 67.5 = 127.5 miles.
4
Calculate the distance of the return route.
102102 miles
The return route is 20% shorter than the outbound trip. This means it is 100%−20%=80%100\% - 20\% = 80\% of the outbound distance. Multiply: 127.5×0.8=102127.5 \times 0.8 = 102 miles.
5
Calculate the total distance traveled for the entire round trip.
229.5229.5 miles
Add the total outbound distance and the return distance: 127.5+102=229.5127.5 + 102 = 229.5 miles.

Key Concept

Calculating total distance across multiple legs with varying speeds, mixed time units, and percent reductions.
Estimated Time:3m 0s
Question 20Question →

A rescue helicopter flies at a rate of 33 miles per minute for 4040 minutes to reach an extraction point. After the pickup, it flies to a hospital at a cruising speed of 120120 miles per hour for 9090 minutes. What is the total distance the helicopter traveled in miles?

Show answer & explanation

Answer: 300

Answer

The correct answer is 300 miles, which is the sum of the 120 miles traveled in the first stage and the 180 miles traveled in the second stage.
The correct answer accurately accounts for the units in both stages of the flight. For the first stage, the units match (miles per minute and minutes), yielding 120 miles. For the second stage, 90 minutes is converted to 1.5 hours to match the miles per hour speed, yielding 180 miles. Adding them together gives 300 miles.

Step-by-Step Solution

1
Calculate the distance for the first stage by multiplying the rate by the time.
33 miles/minute × 4040 minutes = 120120 miles.
The rate is given in miles per minute and the time is given in minutes, so the units already match and no time conversion is necessary.
2
Convert the time for the second stage from minutes to hours.
9090 minutes ÷ 6060 minutes/hour = 1.51.5 hours.
The cruising speed is given in miles per hour, so the travel time must be converted to hours before calculating distance.
3
Calculate the distance for the second stage using the converted time.
120120 miles/hour × 1.51.5 hours = 180180 miles.
Multiplying the speed in mph by the time in hours yields the distance in miles.
4
Add the distances from both stages to find the total distance traveled.
120120 miles + 180180 miles = 300300 miles.
The total distance of a multi-leg journey is the sum of the distances of each individual leg.

Key Concept

Calculating multi-leg distances requiring attention to varying speed units and necessary time conversions.
Estimated Time:2m 0s
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Calculating Distance Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) | Examkin