Time, Rate, and Distance Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 4

Question 61Question →

A Navy coastal patrol boat is assigned a $360$ -nautical-mile mission. It navigates the first $120$ nautical miles through restricted waters at an average speed of $30$ knots. It then travels the remaining $240$ nautical miles through open ocean at an average speed of $40$ knots. Determine the boat's overall average speed for the entire mission.

Fill in the blanks below

The boat's overall average speed for the entire mission is knots.

Show answer & explanation

Answer

The overall average speed is 36 knots.

The correct overall average speed is determined by calculating the total distance covered (

360

nautical miles) divided by the total time taken (

10

hours). First, find the time for each leg:

120

nautical miles at

30

knots takes

4

hours, and

240

nautical miles at

40

knots takes

6

hours. The total time is

10

hours. Therefore, the average speed is

360 \div 10 = 36

knots.

Step-by-Step Solution

1

Calculate the time spent navigating the first segment.

4

hours

Time is equal to distance divided by speed (

120 \div 30 = 4

).

2

Calculate the time spent traveling the second segment.

6

hours

Time is equal to distance divided by speed (

240 \div 40 = 6

).

3

Calculate the total time for the entire mission.

10

hours

Adding the time from both segments gives the total mission time (

4 + 6 = 10

).

4

Calculate the overall average speed.

36

knots

Overall average speed is the total distance divided by the total time (

360 \div 10 = 36

).

Key Concept

To find overall average speed for a trip with multiple segments, divide the total distance by the total time, rather than averaging the individual speeds.

Question 62Question →

A logistics company dispatches a delivery van traveling on a straight highway at a constant speed of $40$ mph. Exactly $90$ minutes later, a courier is dispatched from the same location to intercept the van, traveling on the same highway at a constant speed of $60$ mph. How many hours will it take the courier to catch up to the delivery van after departing?

4.5

0.6

3

1.8

Show answer & explanation

Answer: $3$

Answer

It will take

3

hours for the courier to catch up to the delivery van.

First, the van's head start of 90 minutes must be converted to 1.5 hours. Traveling at 40 mph for 1.5 hours puts the van 60 miles ahead of the starting point. Next, because the vehicles travel in the same direction, their relative speed is the difference between their individual speeds: 60 mph - 40 mph = 20 mph. This means the courier gains 20 miles on the van every hour. Finally, divide the 60-mile gap by the 20 mph relative speed to find the time: 60 / 20 = 3 hours.

Step-by-Step Solution

1

Convert the van's head start time from minutes to hours.

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

Speed is given in miles per hour (mph), so all time units must be in hours to maintain consistency.

2

Calculate the initial distance gap created by the van's head start.

40 \text{ mph} \times 1.5 \text{ hours} = 60 \text{ miles}

Distance equals rate multiplied by time. This is the gap the courier must close.

3

Determine the relative speed of the courier closing the gap.

60 \text{ mph} - 40 \text{ mph} = 20 \text{ mph}

Because both vehicles are moving in the same direction, subtract the van's speed from the courier's speed to find how fast the distance between them is shrinking.

4

Calculate the time required for the courier to close the initial gap.

60 \text{ miles} / 20 \text{ mph} = 3 \text{ hours}

Time equals distance divided by rate. Dividing the initial gap by the relative speed gives the catch-up time.

Key Concept

Relative motion in the same direction requires subtracting the speed of the slower object from the faster object to find the relative rate of closure.

Estimated Time:1m 30s

Question 63Question →

A passenger train leaves West Station heading east toward East Station, which is $270$ miles away, traveling at a constant speed of $60$ mph. Exactly $1$ hour later, a freight train leaves East Station heading west toward West Station on a parallel track at a constant speed of $45$ mph. How many hours after the passenger train's departure will the two trains pass each other?

Show answer & explanation

Answer: 3

Answer

3 hours

The passenger train travels 60 miles in its first hour, leaving 210 miles between the trains. Traveling toward each other, their combined relative speed is 105 mph. It takes them 2 hours to cover the 210 miles together. Adding the initial 1 hour, the total time since the passenger train departed is 3 hours.

Step-by-Step Solution

1

Calculate the distance covered by the passenger train during its 1-hour head start.

60 \text{ mph} \times 1 \text{ hour} = 60 \text{ miles}

This establishes how much distance is covered before the second train begins moving.

2

Find the remaining distance between the two trains.

270 \text{ miles} - 60 \text{ miles} = 210 \text{ miles}

This is the remaining gap the two trains must close together once both are moving.

3

Calculate the combined (relative) speed of the two trains.

60 \text{ mph} + 45 \text{ mph} = 105 \text{ mph}

Because they are traveling toward each other from opposite directions, their speeds add up to close the distance.

4

Determine the time it takes to close the remaining 210 miles.

210 \text{ miles} \div 105 \text{ mph} = 2 \text{ hours}

Using the formula Time = Distance / Rate.

5

Calculate the total time since the passenger train's departure.

1 \text{ hour} + 2 \text{ hours} = 3 \text{ hours}

The question specifically asks for the time after the passenger train's departure, which includes its initial 1-hour head start.

Key Concept

Relative motion and converging objects with staggered start times

Question 64Question →

A military transport convoy departs from a base and travels on a straight route at a constant speed of $30$ mph. Exactly $15$ minutes later, a tactical vehicle is dispatched along the same route to deliver updated orders, traveling at a constant speed of $45$ mph. How many minutes will it take for the tactical vehicle to catch up to the convoy from the time the tactical vehicle departs?

6

60

30

300

Show answer & explanation

Answer: 30

Answer

30

The correct answer accurately calculates the

7.5

-mile head start distance (

30 \text{ mph} \times 0.25 \text{ hours}

) and divides it by the

15

mph relative speed (

45 \text{ mph} - 30 \text{ mph}

) to find a catch-up time of

0.5

hours, which equals

30

minutes.

Step-by-Step Solution

1

Convert the convoy's head start time from minutes to hours.

15 \text{ minutes} = 0.25 \text{ hours}

.

Vehicle speeds are given in miles per hour (mph), so the time must be converted to hours for unit consistency.

2

Calculate the distance the convoy traveled during its head start.

30 \text{ mph} \times 0.25 \text{ hours} = 7.5 \text{ miles}

.

This establishes the initial distance gap that the tactical vehicle needs to close.

3

Determine the relative catch-up speed of the tactical vehicle.

45 \text{ mph} - 30 \text{ mph} = 15 \text{ mph}

.

Because the vehicles are traveling in the same direction, you subtract the slower speed from the faster speed to find the rate at which the gap is closing.

4

Calculate the time required to close the gap in hours.

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

.

Time equals distance divided by rate (

t = \frac{d}{r}

).

5

Convert the catch-up time back to minutes.

0.5 \text{ hours} \times 60 \text{ minutes/hour} = 30 \text{ minutes}

.

The question specifically asks for the time in minutes.

Key Concept

Catch-up scenarios require calculating the initial distance gap and dividing it by the relative speed (the difference in speeds) between the two moving objects.

Question 65Question →

A scout rover leaves a forward operating base and travels along a straight path at a constant speed of $40$ mph. Exactly $30$ minutes later, a heavily armored command vehicle leaves the same base along the same path at a constant speed of $55$ mph to overtake the rover. How many minutes will the command vehicle need to drive before it catches up to the scout rover?

Show answer & explanation

Answer: 80; 80 minutes; 80 mins; eighty

Answer

80

The scout rover establishes a 20-mile lead during its 30-minute (0.5 hour) head start. The command vehicle closes this 20-mile gap at a relative speed of 15 mph (55 mph - 40 mph). It takes 4/3 hours to close the gap, which converts to exactly 80 minutes.

Step-by-Step Solution

1

Convert the rover's head start time from minutes to hours.

30

minutes is equal to

0.5

hours.

Speed is given in miles per hour (mph), so time must be in hours to accurately calculate the distance.

2

Calculate the head start distance of the scout rover.

40 \text{ mph} \times 0.5 \text{ hours} = 20 \text{ miles}

.

This establishes the initial gap that the command vehicle must close.

3

Calculate the relative catch-up speed.

55 \text{ mph} - 40 \text{ mph} = 15 \text{ mph}

.

Since both vehicles are traveling in the same direction, subtract the slower speed from the faster speed to find how fast the gap is closing.

4

Calculate the time required to catch up in hours.

20 \text{ miles} \div 15 \text{ mph} = \frac{4}{3} \text{ hours}

.

Time equals distance divided by rate.

5

Convert the catch-up time back to minutes.

\frac{4}{3} \times 60 = 80 \text{ minutes}

.

The question specifically asks for the driving time in minutes.

Key Concept

Relative Motion and Catch-Up Scenarios

Question 66Question →

Two rescue helicopters, operating in the same coastal region, are $360$ miles apart. They take off at the same time and fly directly toward each other. Helicopter A flies at a constant speed of $110$ mph, and Helicopter B flies at a constant speed of $130$ mph. How many minutes will it take for the two helicopters to meet?

1080

180

90

110

Show answer & explanation

Answer: 90

Answer

It will take 90 minutes for the two helicopters to meet.

The correct answer is 90. When two objects travel directly toward each other, their relative rate is the sum of their individual speeds. The combined speed is

110 + 130 = 240

mph. The time to meet is the total distance divided by the relative speed:

360 / 240 = 1.5

hours. Finally, to convert hours to minutes, multiply by 60:

1.5 \times 60 = 90

minutes.

Step-by-Step Solution

1

Calculate the combined relative speed of the two helicopters.

110 + 130 = 240

mph

When two objects are moving directly toward each other, their relative speed is the sum of their individual speeds.

2

Calculate the time in hours it takes for them to meet.

360 / 240 = 1.5

hours

Time is equal to the total distance divided by the relative speed.

3

Convert the time from hours to minutes.

1.5 \times 60 = 90

minutes

The question specifically asks for the time in minutes.

Key Concept

Relative Motion and Time Conversion

Question 67Question →

During a naval training exercise, a submarine travels submerged in a straight line at a constant speed of $15$ knots. Exactly $2$ hours later, a destroyer departs from the same location and pursues the submarine along the exact same path at a constant speed of $25$ knots. How many hours will it take for the destroyer to overtake the submarine from the time the destroyer begins moving?

Show answer & explanation

Answer: 3

Answer

It will take 3 hours for the destroyer to catch up to the submarine.

To solve a catch-up scenario, first determine the initial distance between the two objects. The submarine travels at

15

knots for

2

hours, creating a

30

nautical mile gap. Next, find the relative speed by subtracting the slower speed from the faster speed (

25 - 15 = 10

knots) because they are moving in the same direction. Finally, divide the initial gap by the relative speed (

30 \div 10 = 3

) to find the time it takes the destroyer to close the gap.

Step-by-Step Solution

1

Calculate the head-start distance of the submarine.

30

nautical miles

The submarine travels at

15

knots for

2

hours before the destroyer starts.

2

Calculate the relative catch-up speed.

10

knots

The destroyer travels in the same direction, so the relative speed is the difference between their speeds (

25 - 15

).

3

Calculate the time required to close the distance gap.

3

hours

Time equals distance divided by relative rate. Dividing the

30

nautical mile gap by the relative speed of

10

knots gives

3

hours.

Key Concept

Relative Motion and Catch-Up Scenarios

Question 68Question →

A passenger train is traveling at a constant speed of $132 \text{ feet per second}$ . Given that $1 \text{ mile} = 5,280 \text{ feet}$ , how many miles will the train travel in $15 \text{ minutes}$ ?

0.375

22.5

37.5

1,980

Show answer & explanation

Answer: 22.5

Answer

22.5

To find the distance, the units for time and distance must be aligned. Because the train's speed is

132 \text{ feet per second}

, first convert the

15 \text{ minutes}

of travel time into seconds:

15 \times 60 = 900 \text{ seconds}

. Next, calculate the total distance in feet by multiplying the speed by the time:

132 \times 900 = 118,800 \text{ feet}

. Finally, divide this total by

5,280

to convert feet into miles, yielding

22.5 \text{ miles}

.

Step-by-Step Solution

1

Convert the travel time from minutes to seconds.

15 \text{ minutes} \times 60 \text{ seconds/minute} = 900 \text{ seconds}

The speed is given in feet per second, so the time must be in seconds to calculate the distance.

2

Calculate the total distance traveled in feet.

132 \text{ feet/second} \times 900 \text{ seconds} = 118,800 \text{ feet}

Distance is the product of rate and time.

3

Convert the total distance from feet to miles.

118,800 \text{ feet} \div 5,280 \text{ feet/mile} = 22.5 \text{ miles}

The question asks for the final distance in miles.

Key Concept

Converting between different units of time and distance to calculate total distance traveled.

Question 69Question →

During a surveillance operation, a drone flies steadily at a rate of $90 \text{ miles per hour}$ . Given that $1 \text{ mile} = 5,280 \text{ feet}$ , how many feet does the drone cover every second?

Show answer & explanation

Answer: 132; 132 feet; 132 ft; 132 feet per second; 132 ft/s; 132 fps; 132 ft/sec

Answer

132

The drone's speed is

90 \text{ miles per hour}

. First, convert the distance from miles to feet:

90 \text{ miles} \times 5,280 \text{ feet/mile} = 475,200 \text{ feet}

. This is the distance traveled in one hour. Because there are

60 \text{ minutes}

in an hour and

60 \text{ seconds}

in a minute, one hour equals

3,600 \text{ seconds}

. To find the distance traveled in one second, divide the total feet by the total seconds:

475,200 \div 3,600 = 132 \text{ feet}

.

Step-by-Step Solution

1

Determine the distance the drone travels in one hour in feet.

90 \times 5,280 = 475,200 \text{ feet per hour}

Since there are

5,280 \text{ feet}

in one mile, multiplying the speed in miles per hour by

5,280

converts the distance unit from miles to feet.

2

Determine the number of seconds in one hour.

60 \times 60 = 3,600 \text{ seconds}

There are

60 \text{ minutes}

in an hour and

60 \text{ seconds}

in a minute.

3

Calculate the distance covered in one second.

475,200 \div 3,600 = 132 \text{ feet per second}

Dividing the total distance covered in one hour by the total number of seconds in one hour gives the speed in feet per second.

Key Concept

To convert a rate from miles per hour to feet per second, multiply the distance by

5,280

(feet per mile) and divide the time by

3,600

(seconds per hour).

Question 70Question →

A rescue helicopter is flying to a distress signal at a constant speed of $120 \text{ miles per hour}$ . Given that $1 \text{ mile} = 5,280 \text{ feet}$ , how many feet does the helicopter travel in $45 \text{ seconds}$ ?

5,400

7,920

285,120

475,200

Show answer & explanation

Answer: 7,920

Answer

7,920

The problem requires finding the distance in feet, given a speed in miles per hour and time in seconds. First, convert the speed to feet per second. Since there are

5,280 \text{ feet}

in a mile,

120 \text{ miles per hour}

is

120 \times 5,280 = 633,600 \text{ feet per hour}

. Since there are

3,600 \text{ seconds}

in an hour, the speed is

633,600 \div 3,600 = 176 \text{ feet per second}

. Finally, multiply this rate by the time of

45 \text{ seconds}

to get the distance:

176 \times 45 = 7,920 \text{ feet}

.

Step-by-Step Solution

1

Convert the helicopter's speed from miles per hour to feet per hour.

120 \times 5,280 = 633,600 \text{ feet per hour}

To align the distance unit (miles) with the requested final unit (feet).

2

Convert the speed from feet per hour to feet per second.

633,600 \div 3,600 = 176 \text{ feet per second}

There are

60 \times 60 = 3,600

seconds in an hour, and the given elapsed time is in seconds.

3

Calculate the total distance traveled in

45 \text{ seconds}

.

176 \times 45 = 7,920 \text{ feet}

Distance equals rate multiplied by time (

D = R \times T

).

Key Concept

Unit Conversions in Motion Problems

Question 71Question →

An industrial conveyor belt moves continuously at a steady speed of $44 \text{ feet per minute}$ . Given that $1 \text{ mile} = 5,280 \text{ feet}$ , how many miles does a package travel if it remains on the belt for exactly $10 \text{ hours}$ ?

Show answer & explanation

Answer: 5; 5 miles; five; five miles

Answer

5

To find the total distance traveled in miles, unit conversions must be applied to align the given measurements. The speed is given in feet per minute, but the time is in hours and the requested distance is in miles. First, multiply the speed by 60 to convert it to feet per hour (

44 \times 60 = 2,640 \text{ feet per hour}

). Next, convert this speed into miles per hour by dividing by the number of feet in a mile (

2,640 \div 5,280 = 0.5 \text{ miles per hour}

). Finally, multiply this speed by the total time (

0.5 \text{ mph} \times 10 \text{ hours}

) to find that the package travels a total distance of 5 miles.

Step-by-Step Solution

1

Convert the speed from feet per minute to feet per hour.

44 \text{ feet/minute} \times 60 \text{ minutes/hour} = 2,640 \text{ feet/hour}

The travel time is given in hours, so the speed needs to reflect distance per hour to maintain consistent units of time.

2

Convert the speed from feet per hour to miles per hour.

2,640 \text{ feet/hour} \div 5,280 \text{ feet/mile} = 0.5 \text{ miles/hour}

The final requested distance is in miles, so converting the rate into miles per hour simplifies the final distance calculation.

3

Calculate the total distance traveled.

0.5 \text{ miles/hour} \times 10 \text{ hours} = 5 \text{ miles}

Multiplying the constant rate in miles per hour by the total time in hours yields the total distance in miles.

Key Concept

Unit Conversions in Motion Problems

Alternative Method

Instead of converting the speed to miles per hour first, you can convert the total time into minutes:

10 \text{ hours} \times 60 \text{ minutes/hour} = 600 \text{ minutes}

. Then, find the total distance in feet:

600 \text{ minutes} \times 44 \text{ feet/minute} = 26,400 \text{ feet}

. Finally, divide by

5,280

to convert to miles:

26,400 \div 5,280 = 5 \text{ miles}

.

Estimated Time:1m 30s

Question 72Question →

An interstate bus travels from a central terminal to a destination city $150$ miles away and immediately returns along the same route. The bus averages a fuel efficiency of $12$ miles per gallon. If the bus starts the journey with exactly $60$ gallons of fuel, how many gallons of fuel will remain in the tank at the end of the round trip?

25

35

47.5

57.5

Show answer & explanation

Answer: 35

Answer

There will be 35 gallons of fuel remaining in the tank.

The correct answer is derived by first finding the total round-trip distance, which is

150 \times 2 = 300

miles. Dividing this distance by the fuel efficiency of

12

miles per gallon gives the total fuel consumed:

300 \div 12 = 25

gallons. Finally, subtracting the consumed fuel from the initial

60

gallons yields the remaining amount:

60 - 25 = 35

gallons.

Step-by-Step Solution

1

Calculate the total distance for the round trip.

150 miles * 2 = 300 miles

The bus travels to the destination and returns, meaning the one-way distance must be doubled.

2

Determine the total fuel consumed during the entire trip.

300 miles / 12 miles per gallon = 25 gallons

Dividing the total distance by the fuel efficiency gives the total amount of fuel required.

3

Calculate the remaining fuel in the tank.

60 gallons - 25 gallons = 35 gallons

Subtracting the consumed fuel from the initial fuel amount provides the remaining balance.

Key Concept

Calculating remaining fuel by finding the total round-trip distance, dividing by fuel efficiency to find consumed fuel, and subtracting from initial capacity.

Question 73Question →

A maritime supply vessel consumes fuel at a rate of $2.5$ gallons per mile. The vessel leaves its home port with exactly $500$ gallons of fuel to complete a round-trip delivery to an offshore research station located $70$ miles away. Assuming the fuel consumption rate remains constant, how many gallons of fuel will remain in the tank when the vessel returns to its home port?

150

325

444

465

Show answer & explanation

Answer: $150$

Answer

150 gallons

The total distance for the round trip is 140 miles (70 miles each way). Multiplying this distance by the consumption rate of 2.5 gallons per mile gives a total fuel usage of 350 gallons. Subtracting the 350 gallons used from the initial 500 gallons leaves 150 gallons of fuel remaining.

Step-by-Step Solution

1

Calculate the total round-trip distance.

70 \times 2 = 140

miles

The vessel must travel to the station and back to the home port.

2

Determine the total amount of fuel consumed.

140 \times 2.5 = 350

gallons

Multiply the total miles by the gallons consumed per mile to find the overall fuel usage.

3

Calculate the remaining fuel in the tank.

500 - 350 = 150

gallons

Subtract the total fuel consumed from the starting amount of fuel.

Key Concept

Calculating total fuel consumption based on distance and burn rate, and applying it to a starting capacity.

Question 74Question →

Match each vehicle's fuel scenario to its calculated maximum usable travel range.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Delivery van matches to

320

miles, heavy transport truck matches to

375

miles, fleet car matches to

420

miles, and rural mail carrier matches to

270

miles.

Each vehicle's range is successfully calculated by isolating the total usable fuel and applying its specific rate of fuel consumption (such as miles per gallon).

Step-by-Step Solution

1

Calculate the usable range for the delivery van.

The van has

20

usable gallons (

25 - 5

). Multiplying by

16

mpg gives

320

miles.

The

5

-gallon reserve must be subtracted before multiplying by the fuel efficiency.

2

Calculate the usable range for the heavy transport truck.

The truck travels

25

miles per

3

gallons. With

45

gallons, it can make

15

sets of this distance (

45 \div 3 = 15

).

15 \times 25 = 375

miles.

Setting up a direct proportion allows for finding total distance based on the consumption rate.

3

Calculate the usable range for the fleet car.

The car's efficiency is

180 \div 6 = 30

mpg. With

14

gallons, the range is

14 \times 30 = 420

miles.

Finding the unit rate (mpg) first makes it easy to multiply by the total fuel capacity.

4

Calculate the usable range for the rural mail carrier.

The carrier's efficiency is

60 \div 4 = 15

mpg. With

18

gallons, the range is

18 \times 15 = 270

miles.

Similar to the fleet car, dividing distance by gallons used provides the unit rate needed to find the maximum range.

Key Concept

Calculating distance by determining fuel efficiency (unit rate) and multiplying it by the available usable fuel.

Question 75Question →

An armored transport vehicle has a $50$ -gallon fuel tank and averages $20$ miles per gallon on paved roads. When driving on unpaved terrain, its fuel efficiency drops to $12$ miles per gallon. The vehicle begins a mission with a completely full tank and drives $160$ miles on paved roads before switching to unpaved terrain for the remainder of the trip. If the vehicle reaches its destination with exactly $12$ gallons of fuel remaining, how many miles did it travel on the unpaved terrain?

360

456

504

600

Show answer & explanation

Answer: $360$

Answer

The vehicle traveled

360

miles on the unpaved terrain.

To find the distance traveled on unpaved terrain, we must isolate the fuel used exclusively for that portion. The vehicle started with

50

gallons and ended with

12

gallons, meaning

38

gallons were used overall. The

160

-mile paved segment at

20

mpg consumed

8

gallons. Subtracting these

8

gallons from the

38

total used leaves

30

gallons burned on the unpaved terrain. Multiplying

30

gallons by the unpaved efficiency of

12

mpg results in

360

miles.

Step-by-Step Solution

1

Calculate the fuel consumed on the paved roads.

160 \text{ miles} \div 20 \text{ mpg} = 8 \text{ gallons}

.

This establishes how much fuel was removed from the tank before the vehicle hit the unpaved terrain.

2

Calculate the total amount of fuel consumed during the entire mission.

50 \text{ gallons} - 12 \text{ gallons} = 38 \text{ gallons}

.

Subtracting the remaining fuel from the starting capacity gives the total fuel burned across both terrain types.

3

Determine the fuel used specifically on the unpaved terrain.

38 \text{ gallons} - 8 \text{ gallons} = 30 \text{ gallons}

.

Subtracting the paved road fuel usage from the total fuel usage isolates the fuel dedicated to the unpaved portion of the trip.

4

Calculate the distance traveled on the unpaved terrain.

30 \text{ gallons} \times 12 \text{ mpg} = 360 \text{ miles}

.

Multiplying the fuel used by the specific fuel efficiency for that terrain yields the correct distance.

Key Concept

Multi-segment fuel consumption and efficiency rate changes.

Question 76Question →

A heavy equipment transporter has a maximum fuel capacity of $250$ gallons and operates with a fuel efficiency of $4$ miles per gallon. The vehicle is dispatched to deliver cargo to a remote site and immediately return to its base along the same route. Military regulations require the transporter to arrive back at base with a minimum of $50$ gallons of fuel in reserve. What is the maximum one-way distance, in miles, the transporter can travel to the remote site without refueling?

Show answer & explanation

Answer: 400

Answer

The maximum one-way distance the transporter can travel is 400 miles.

The correct answer is derived by first identifying the usable fuel (250 - 50 = 200 gallons). Next, the total round-trip distance is calculated by multiplying the usable fuel by the fuel efficiency (200 gallons * 4 miles/gallon = 800 miles). Finally, since the vehicle must travel to the site and return, the total range is divided by 2, resulting in a maximum one-way distance of 400 miles.

Step-by-Step Solution

1

Determine the amount of usable fuel available for the mission.

200 gallons

The transporter has a 250-gallon tank but must retain a 50-gallon reserve upon return, meaning only 200 gallons can be consumed during the trip.

2

Calculate the total distance the vehicle can travel using the usable fuel.

800 miles

Multiplying the 200 gallons of usable fuel by the vehicle's fuel efficiency of 4 miles per gallon gives the total range.

3

Determine the maximum one-way distance.

400 miles

Because the mission is a round trip along the same route, the total range must cover the distance to the site and back. Therefore, the one-way distance is half of the total range.

Key Concept

Calculating one-way distance using fuel efficiency, total fuel capacity, required reserves, and accounting for round-trip constraints.

Question 77Question →

A cargo transport truck travels from a central depot to a regional distribution center $120$ miles away and returns to the depot along the same route. The truck operates with a fuel efficiency of $15$ miles per gallon. If diesel fuel costs $\$3.50$ per gallon, what is the total fuel cost for this complete round trip?

\$28.00

\$5.60

\$56.00

\$16.00

Show answer & explanation

Answer: $\$56.00$

Answer

The total fuel cost for the complete round trip is

\$56.00

.

The total distance for the round trip is twice the one-way distance (

240

miles). Dividing this distance by the fuel efficiency (

15

miles per gallon) gives the total fuel consumed, which is

16

gallons. Finally, multiplying the

16

gallons by the unit price of

\$3.50

per gallon results in the correct total cost of

\$56.00

.

Step-by-Step Solution

1

Calculate the total distance driven for the round trip.

120 \times 2 = 240

miles

The truck travels to the center and returns along the same route, so the one-way distance must be doubled.

2

Calculate the total amount of fuel consumed.

240 \div 15 = 16

gallons

Dividing the total distance by the fuel efficiency (miles per gallon) gives the total volume of fuel used.

3

Calculate the final monetary cost of the fuel.

16 \times \$3.50 = \$56.00

Multiplying the total gallons consumed by the price per gallon yields the total cost.

Key Concept

Fuel Efficiency and Range

Alternative Method

You can also calculate the fuel cost per mile first:

\$3.50

per gallon

\div 15

miles per gallon =

\$0.2333...

per mile. Then multiply this per-mile cost by the total round-trip distance of

240

miles to arrive at the

\$56.00

total.

Estimated Time:45s

Question 78Question →

A courier travels from the office to a client's location $40$ miles away. The trip there takes $1$ hour. The return trip along the same route takes $4$ hours due to heavy traffic. What is the courier's average speed for the entire round trip?

8

mph

10

mph

16

mph

25

mph

Show answer & explanation

Answer: $16$ mph

Answer

16

mph

The correct answer is found by dividing the total distance for the round trip (

40

miles outbound +

40

miles return =

80

miles) by the total time taken (

1

hour +

4

hours =

5

hours). This gives an average speed of

80 \div 5 = 16

mph.

Step-by-Step Solution

1

Calculate the total distance for the round trip.

40 + 40 = 80

miles

Average speed calculation requires the total distance traveled during the entire journey.

2

Calculate the total time for the round trip.

1 + 4 = 5

hours

Average speed calculation requires the total time elapsed.

3

Divide the total distance by the total time to find the average speed.

80 \div 5 = 16

mph

The formula for average speed is Total Distance divided by Total Time.

Key Concept

The average speed for a round trip is calculated by dividing the total round-trip distance by the total time taken. It is not the simple arithmetic average of the speeds for each leg.

Question 79Question →

A delivery truck travels from a warehouse to a distribution center at an average speed of $40$ mph and returns along the same route at an average speed of $60$ mph. If the entire round trip takes $5$ hours, what is the total round-trip distance traveled by the truck?

120

miles

240

miles

250

miles

500

miles

Show answer & explanation

Answer: $240$ miles

Answer

The correct total round-trip distance is

240

miles.

The total time is the sum of the time for each leg. Letting

d

be the one-way distance, the equation is

\frac{d}{40} + \frac{d}{60} = 5

. Solving this gives a one-way distance of

d = 120

miles. Since the question asks for the total round-trip distance, this must be doubled to get

240

miles.

Step-by-Step Solution

1

Set up an equation for the total time of the trip.

Let

d

be the one-way distance. Time is equal to Distance divided by Speed. Therefore, the total time equation is

\frac{d}{40} + \frac{d}{60} = 5

.

The total round-trip time is the sum of the time spent on the outbound leg and the return leg.

2

Find a common denominator to add the fractions.

The least common multiple of

40

and

60

is

120

. Convert the fractions:

\frac{3d}{120} + \frac{2d}{120} = 5

.

Fractions must have a common denominator before they can be algebraically combined.

3

Combine the fractions and solve for the one-way distance

d

.

\frac{5d}{120} = 5

, which simplifies to

\frac{d}{24} = 5

. Multiplying both sides by

24

yields

d = 120

miles.

This isolates the variable

d

to determine the distance of a single leg of the journey.

4

Calculate the total round-trip distance.

Total distance =

2d = 2 \times 120 = 240

miles.

The question specifically asks for the total round-trip distance, which is twice the one-way distance.

Key Concept

To find distances in round trips with different speeds, set up an equation using the relationship Time = Distance / Speed for each leg, taking care to answer the specific question asked (one-way vs. total distance).

Estimated Time:1m 30s

Question 80Question →

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?

127.5 miles

153.0 miles

213.3 miles

229.5 miles

Show answer & explanation

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 = 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.

60

miles

Convert 1 hour 20 minutes into hours:

1 + \frac{20}{60} = 1 + \frac{1}{3} = \frac{4}{3}

hours. Multiply by speed:

45 \times \frac{4}{3} = 60

miles.

2

Calculate the distance covered during the second travel segment.

67.5

miles

Convert 2 hours 15 minutes into hours:

2 + \frac{15}{60} = 2 + \frac{1}{4} = 2.25

hours. Multiply by speed:

30 \times 2.25 = 67.5

miles. (The 45-minute rest adds 0 distance).

3

Find the total outbound distance to Camp Bravo.

127.5

miles

Add the distances from the first and second segments:

60 + 67.5 = 127.5

miles.

4

Calculate the distance of the return route.

102

miles

The return route is 20% shorter than the outbound trip. This means it is

100\% - 20\% = 80\%

of the outbound distance. Multiply:

127.5 \times 0.8 = 102

miles.

5

Calculate the total distance traveled for the entire round trip.

229.5

miles

Add the total outbound distance and the return distance:

127.5 + 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

Time, Rate, and Distance

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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Key Concept

Common Mistakes

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Key Concept

Common Mistakes

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Key Concept

Common Mistakes

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

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Key Concept

Common Mistakes

Alternative Method

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Common Mistakes

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

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Key Concept

Common Mistakes

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

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Answer

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Key Concept

Common Mistakes

Answer

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Key Concept

Common Mistakes

Answer