Time, Rate, and Distance Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

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

Show answer & explanation

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\text{ miles per hour}

by

\frac{2}{3}\text{ of an hour}

yields a total distance of

240\text{ miles}

.

Step-by-Step Solution

1

Convert the travel time from minutes to 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 \times Time

.

240\text{ miles}

Multiplying the constant rate of

360\text{ mph}

by the travel time of

\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\text{ miles}

by

60\text{ minutes}

, which equals

6\text{ miles per minute}

. Then, multiply

6\text{ miles per minute}

by

40\text{ minutes}

to get

240\text{ miles}

.

Estimated Time:45s

Question 2Question →

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

Show answer & explanation

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 →

Match each military travel scenario with its calculated average speed or travel time.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The matches are: convoy speed is 45 mph, patrol boat time is 30 minutes, helicopter speed is 160 mph, and humvee time is 120 minutes.

Each scenario requires applying the fundamental relationship between distance, rate, and time (

d = rt

). For scenarios asking for minutes, the calculated hours are multiplied by 60. For scenarios given in minutes but requiring mph, the minutes are divided by 60.

Step-by-Step Solution

1

Calculate the speed for the convoy.

180 \text{ miles} \div 4 \text{ hours} = 45 \text{ mph}

Average speed is found by dividing total distance by total time.

2

Calculate the travel time for the patrol boat.

15 \text{ miles} \div 30 \text{ mph} = 0.5 \text{ hours}

.

0.5 \times 60 = 30 \text{ minutes}

.

Time is distance divided by rate. The result in hours must be multiplied by 60 to find minutes.

3

Calculate the speed for the helicopter.

90 \text{ minutes} = 1.5 \text{ hours}

.

240 \text{ miles} \div 1.5 \text{ hours} = 160 \text{ mph}

.

Speed in mph requires the time to be in hours, so minutes are divided by 60 first.

4

Calculate the travel time for the humvee.

110 \text{ miles} \div 55 \text{ mph} = 2 \text{ hours}

.

2 \times 60 = 120 \text{ minutes}

.

Divide distance by rate to get hours, then multiply by 60 for minutes.

Key Concept

Calculating Rate and Time with Unit Conversions

Estimated Time:1m 30s

Question 4Question →

A cargo plane travels at a constant speed of $300\text{ miles per hour}$ . At this rate, how many miles does the plane travel in $20\text{ minutes}$ ?

15

60

100

6,000

Show answer & explanation

Answer: $100$

Answer

100

The correct answer correctly converts the travel time to hours by recognizing that

20\text{ minutes}

is exactly one-third (

\frac{1}{3}

) of an hour. Multiplying the rate of

300\text{ miles per hour}

by

\frac{1}{3}\text{ of an hour}

gives a total distance of

100\text{ miles}

.

Step-by-Step Solution

1

Convert the given time from minutes to hours.

20\text{ minutes} = \frac{20}{60}\text{ hours} = \frac{1}{3}\text{ hour}

The speed is given in miles per hour, so the time must be in hours before multiplying.

2

Calculate the distance using the formula Distance = Rate × Time.

300 \times \frac{1}{3} = 100\text{ miles}

Multiplying the constant rate by the elapsed time yields the total distance traveled.

Key Concept

Converting time units to match the rate units before calculating distance.

Estimated Time:45s

Question 5Question →

A family rents an RV for a cross-country road trip. The RV has a fuel tank capacity of $55$ gallons and averages $12$ miles per gallon. If the driver begins with a completely full tank and plans to leave exactly $10$ gallons of fuel in the tank as a safety reserve, what is the maximum number of miles the RV can travel before needing to refuel?

Show answer & explanation

Answer: 540

Answer

540

The correct distance is found by first determining the amount of fuel that can actually be used for the trip. Out of the

55

gallons,

10

must remain in the tank, leaving

45

gallons available. At a rate of

12

miles for every gallon, the RV can travel

45

multiplied by

12

, which equals

540

miles.

Step-by-Step Solution

1

Determine the usable fuel by subtracting the reserve from the total capacity.

55 - 10 = 45

gallons

The driver will not use the bottom 10 gallons of the tank, so this fuel cannot contribute to the travel distance.

2

Calculate the maximum distance using the usable fuel and the fuel efficiency rate.

45 \times 12 = 540

miles

Distance equals the amount of fuel used multiplied by the miles per gallon.

Key Concept

Fuel Efficiency and Range calculations involving partial tank usage and safety reserves.

Alternative Method

You could also calculate the total theoretical distance the RV could travel on a full tank (

55 \times 12 = 660

miles) and subtract the distance that would be covered by the

10

-gallon reserve (

10 \times 12 = 120

miles).

660 - 120 = 540

miles.

Estimated Time:1m 0s

Question 6Question →

A patrol unit drives at a steady speed of $20\text{ mph}$ for $3$ hours along a desert trail. They then enter a paved highway and drive at $50\text{ mph}$ for $2$ hours. What is the total distance traveled by the patrol unit?

Show answer & explanation

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\text{ mph} \times 3\text{ hours} = 60\text{ miles}

. For the second leg, the distance is

50\text{ mph} \times 2\text{ hours} = 100\text{ miles}

. Adding these two distances together (

60 + 100

) gives a total distance of

160

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 \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 \times T

).

Question 7Question →

A military supply truck travels at a steady rate of $40\text{ mph}$ for exactly $45$ minutes along a designated supply route. What is the total distance traveled?

30\text{ miles}

18\text{ miles}

300\text{ miles}

1800\text{ miles}

Show answer & explanation

Answer: $30\text{ miles}$

Answer

30\text{ miles}

To find the correct distance, the time must first be converted to match the units of the rate. Dividing

45\text{ minutes}

by

60

gives

0.75\text{ hours}

. Multiplying the rate (

40\text{ mph}

) by the time (

0.75\text{ hours}

) gives exactly

30\text{ miles}

.

Step-by-Step Solution

1

Convert the travel time from minutes to hours.

45\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\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 8Question →

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

35\text{ nautical miles}

33\text{ nautical miles}

30\text{ nautical miles}

350\text{ nautical miles}

Show answer & explanation

Answer: $35\text{ nautical miles}$

Answer

35\text{ nautical miles}

The correct answer is found by converting the travel time of

2\text{ hours and } 20\text{ minutes}

into

2\frac{1}{3}\text{ hours}

, and then multiplying this time by the speed of

15\text{ knots}

. The calculation is

15 \times \frac{7}{3} = 35\text{ nautical miles}

.

Step-by-Step Solution

1

Convert the travel time into hours.

2\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.

\text{Distance} = 15 \times 2\frac{1}{3} = 15 \times \frac{7}{3} = 35\text{ nautical miles}

.

The formula for distance is

\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 9Question →

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

28.2

31

39.2

67

Show answer & explanation

Answer: $31$

Answer

The correct answer is

31

nautical miles.

The total distance is found by calculating the distance for each leg separately. First, convert the times into hours:

15\text{ minutes}

is

0.25\text{ hours}

(making the first leg

2.25\text{ hours}

), and

12\text{ minutes}

is

0.2\text{ hours}

. Multiplying these times by their respective speeds (

12 \times 2.25

and

20 \times 0.2

) gives distances of

27

and

4

nautical miles. Adding these together yields a total of

31

nautical miles.

Step-by-Step Solution

1

Convert the time of the first leg into hours.

2\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\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\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\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\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 10Question →

During a morning commute, a passenger train maintains a constant speed of $48\text{ miles per hour}$ between two city stations. If the non-stop journey takes exactly $15$ minutes, what is the total distance between the two stations?

12\text{ miles}

7.2\text{ miles}

120\text{ miles}

720\text{ miles}

Show answer & explanation

Answer: $12\text{ miles}$

Answer

The distance between the two stations is

12\text{ miles}

.

The correct answer is found by first converting

15

minutes to hours by dividing by

60

, which gives

0.25

hours. Then, multiplying the speed of

48\text{ miles per hour}

by

0.25

hours results in a distance of

12\text{ miles}

.

Step-by-Step Solution

1

Identify the formula for distance.

Distance = 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 \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 \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 11Question →

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 $60\text{ mph}$ for $2\text{ hours and } 45\text{ minutes}$ . Upon entering the secondary zone, it reduces its speed to $40\text{ mph}$ for the remaining $1\text{ hour and } 15\text{ minutes}$ of the route. What is the total distance traveled by the freight train?

215\text{ miles}

200\text{ miles}

193\text{ miles}

165\text{ miles}

Show answer & explanation

Answer: $215\text{ miles}$

Answer

The freight train traveled a total distance of

215\text{ miles}

.

To find the total distance, each segment must be calculated separately using the formula

\text{Distance} = \text{Speed} \times \text{Time}

. For the primary zone,

2\text{ hours and } 45\text{ minutes}

is

2.75\text{ hours}

. Multiplying

60\text{ mph}

by

2.75\text{ hours}

yields

165\text{ miles}

. For the secondary zone,

1\text{ hour and } 15\text{ minutes}

is

1.25\text{ hours}

. Multiplying

40\text{ mph}

by

1.25\text{ hours}

yields

50\text{ miles}

. The total distance is the sum of these two segments:

165 + 50 = 215\text{ miles}

.

Step-by-Step Solution

1

Convert the travel time for the primary zone into hours.

2\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.

\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\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.

\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\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 = rt

) to each segment and summing the results.

Question 12Question →

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

Show answer & explanation

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 \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 \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\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 13Question →

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

Show answer & explanation

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\text{ hours}

) and then multiplying it by the constant speed (

55\text{ mph}

) to yield exactly

198\text{ miles}

.

Step-by-Step Solution

1

Convert the travel time into a single unit (hours) to match the rate.

3\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 \times 3.6

This formula determines the total distance covered over a specific time frame at a constant speed.

3

Calculate the final distance.

198

Multiplying the constant rate of

55\text{ mph}

by the total duration of

3.6\text{ hours}

yields the total miles traveled.

Key Concept

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

Question 14Question →

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

90\text{ miles}

5,400\text{ miles}

54\text{ miles}

900\text{ miles}

Show answer & explanation

Answer: $90\text{ miles}$

Answer

The total distance traveled by the helicopter is

90\text{ miles}

.

The correct answer accurately converts the

45\text{ minutes}

of flight time into

0.75\text{ hours}

, and then applies the distance formula (

D = R \times T

) to find

120 \times 0.75 = 90\text{ miles}

.

Step-by-Step Solution

1

Convert the flight time from minutes to hours.

45\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

\text{Distance} = \text{Rate} \times \text{Time}

.

120\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 15Question →

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

305\text{ nautical miles}

300\text{ nautical miles}

247\text{ nautical miles}

200\text{ nautical miles}

Show answer & explanation

Answer: $305\text{ nautical miles}$

Answer

305\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\text{ minutes}

is

0.75\text{ hours}

, and

1\text{ hour } 15\text{ minutes}

is

1.25\text{ hours}

. Then, apply the formula

\text{Distance} = \text{Rate} \times \text{Time}

. The first leg is

140\text{ knots} \times 0.75\text{ hours} = 105\text{ nautical miles}

. The hover adds

0

distance. The final leg is

160\text{ knots} \times 1.25\text{ hours} = 200\text{ nautical miles}

. Adding these segments together (

105 + 200

) yields a total distance of

305\text{ nautical miles}

.

Step-by-Step Solution

1

Convert the travel time of the first leg from minutes to hours.

45\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\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\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\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\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\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 16Question →

A squad of soldiers is conducting a foot march along a trail that is $12$ miles long. If they maintain a steady pace of $3$ miles per hour, how many hours will it take them to complete the march?

Show answer & explanation

Answer: 4

Answer

4

Using the fundamental relationship

\text{Time} = \frac{\text{Distance}}{\text{Rate}}

, we divide the total distance of

12

miles by the steady pace of

3

miles per hour. This calculation (

12 \div 3

) results in exactly

4

hours.

Step-by-Step Solution

1

Identify the given values for the distance and the rate of travel.

Distance =

12

miles, Rate =

3

miles per hour.

These values are required to calculate the total elapsed time.

2

Apply the appropriate formula to find the time.

\text{Time} = \frac{\text{Distance}}{\text{Rate}}

Time is equal to total distance divided by the speed.

3

Substitute the values and calculate the result.

\frac{12}{3} = 4

Dividing the distance by the rate gives the total time in hours.

Key Concept

Calculating elapsed time given distance and rate.

Estimated Time:45s

Question 17Question →

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

Show answer & explanation

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\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\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\text{ hour}

and

15\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\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\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 18Question →

A naval submarine travels a total distance of $144$ miles in $4$ hours and $30$ minutes. Assuming a constant rate of travel, which of the following is the average speed of the submarine in miles per hour?

3.2

32

36

648

Show answer & explanation

Answer: $32$

Answer

The average speed is

32

miles per hour.

To find the average speed, the total distance must be divided by the total time in hours. First, convert

4

hours and

30

minutes to

4.5

hours. Then, dividing

144

miles by

4.5

hours gives an average speed of

32

miles per hour.

Step-by-Step Solution

1

Convert the total travel time into a single unit of hours.

4

hours and

30

minutes equals

4.5

hours.

Since the requested speed is in miles per hour, the time must be expressed purely in hours before calculating.

2

Apply the formula for average speed:

Speed = Distance \div Time

.

Speed = 144 \div 4.5

Average speed is found by dividing the total distance traveled by the total time taken.

3

Perform the division.

1440 \div 45 = 32

Shifting the decimal point one place to the right for both the dividend and divisor makes the calculation easier, resulting in

32

miles per hour.

Key Concept

Calculating Rate given Distance and Time

Question 19Question →

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

109.2\text{ nautical miles}

112\text{ nautical miles}

1,120\text{ nautical miles}

6,720\text{ nautical miles}

Show answer & explanation

Answer: $112\text{ nautical miles}$

Answer

112\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\text{ minutes}

is equal to

0.2\text{ hours}

(

12 \div 60

). Adding this to the 3 hours gives a total travel time of

3.2\text{ hours}

. Multiplying the rate of

35\text{ knots}

by

3.2\text{ hours}

yields exactly

112\text{ nautical miles}

.

Step-by-Step Solution

1

Convert the given time into a single unit that matches the rate (hours).

12\text{ minutes} \div 60\text{ minutes/hour} = 0.2\text{ hours}

. Total time =

3.2\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\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 20Question →

Match each travel scenario to the correct amount of time it takes to complete the journey.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The delivery van takes 3 hours, the cargo ship takes 4 hours, the marathon runner takes 2 hours, and the commuter train takes 5 hours.

Each correct match is determined by taking the stated distance in miles and dividing it by the average speed in miles per hour (

t = \frac{d}{r}

). Because the difficulty is intentionally basic, all divisions result in clean, whole-number integer hours.

Step-by-Step Solution

1

Identify the given distance (

d

) and rate (

r

) for each scenario.

Van: (

150

mi,

50

mph), Ship: (

80

mi,

20

mph), Runner: (

16

mi,

8

mph), Train: (

300

mi,

60

mph).

These variables are required to apply the fundamental distance formula.

2

Apply the formula for calculating time:

t = \frac{d}{r}

.

Van:

\frac{150}{50} = 3

. Ship:

\frac{80}{20} = 4

. Runner:

\frac{16}{8} = 2

. Train:

\frac{300}{60} = 5

.

Dividing the total distance traveled by the constant rate yields the total elapsed time.

Key Concept

Calculating elapsed time using the distance-rate-time relationship (

t = \frac{d}{r}

).

Time, Rate, and Distance

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer