Unit Conversions in Motion Problems Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

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 2Question →

A cyclist is riding on a paved trail at a constant speed of $15 \text{ miles per hour}$ . At this rate, how many miles will the cyclist travel in $40 \text{ minutes}$ ?

Show answer & explanation

Answer: 10

Answer

10

The distance is found by matching the time units to the speed units. First, convert

40 \text{ minutes}

into

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

. Then, multiply the speed (

15 \text{ mph}

) by the time (

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

) to get exactly 10 miles.

Step-by-Step Solution

1

Convert the travel time from minutes to hours.

40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}

The speed is given in miles per hour, so the time must be converted to hours before using it in the distance formula.

2

Calculate the total distance traveled.

15 \times \frac{2}{3} = 10 \text{ miles}

Distance is equal to the rate (speed) multiplied by the time (

d = r \times t

).

Key Concept

Unit conversions for time in rate problems

Question 3Question →

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 4Question →

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 5Question →

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 6Question →

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 7Question →

A military convoy is traveling along a straight highway at a constant speed of $45\text{ miles per hour}$ . A scout vehicle leaves the rear of the convoy and travels forward to reach the front of the convoy. The total length of the convoy is $1.5\text{ miles}$ , and the scout vehicle travels at a constant speed of $88\text{ feet per second}$ . How many minutes does it take for the scout vehicle to reach the front of the convoy? ( $1\text{ mile} = 5,280\text{ feet}$ )

0.1

1.5

6

10

Show answer & explanation

Answer: 6

Answer

6

The correct answer is found by equalizing the speed units and analyzing relative motion. First, converting the scout's speed gives

88\text{ ft/s} \times (3600 / 5280) = 60\text{ mph}

. Because the convoy is also moving forward at

45\text{ mph}

, the relative closing speed is

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

. The scout needs to cover the

1.5\text{ mile}

length of the convoy, which takes

1.5\text{ miles} / 15\text{ mph} = 0.1\text{ hours}

. Finally, converting this to minutes yields

0.1 \times 60 = 6\text{ minutes}

.

Step-by-Step Solution

1

Convert the scout vehicle's speed from feet per second to miles per hour.

88\text{ ft/s} \times \frac{3,600\text{ s}}{1\text{ hr}} \div \frac{5,280\text{ ft}}{1\text{ mile}} = 60\text{ mph}

.

To establish a common unit of speed for both vehicles before calculating relative motion.

2

Calculate the relative speed of the scout vehicle compared to the convoy.

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

.

Because both vehicles are moving in the same direction, subtracting the convoy's speed from the scout's speed gives the actual rate at which the scout is catching up (closing speed).

3

Determine the time required to cover the distance of the convoy in hours.

Time = Distance / Rate =

1.5\text{ miles} / 15\text{ mph} = 0.1\text{ hours}

.

Applying the time, rate, and distance formula using the length of the convoy and the relative closing speed.

4

Convert the time from hours to minutes.

0.1\text{ hours} \times 60\text{ minutes/hour} = 6\text{ minutes}

.

The question explicitly asks for the answer in minutes.

Key Concept

Relative Motion and Unit Conversions

Alternative Method

Instead of converting everything to miles and hours, you can convert everything to feet and seconds. Convoy speed =

45\text{ mph} \times (5280 / 3600) = 66\text{ ft/s}

. Relative speed =

88\text{ ft/s} - 66\text{ ft/s} = 22\text{ ft/s}

. Distance =

1.5\text{ miles} \times 5280 = 7,920\text{ feet}

. Time =

7,920\text{ ft} / 22\text{ ft/s} = 360\text{ seconds}

. Finally,

360\text{ seconds} / 60\text{ seconds/minute} = 6\text{ minutes}

.

Estimated Time:3m 0s

Question 8Question →

A naval submarine is traveling underwater at a constant speed of $20\text{ feet per second}$ . At this rate, how many miles will the submarine travel in exactly $1\text{ hour}$ and $6\text{ minutes}$ ?

(Note: $1\text{ mile} = 5,280\text{ feet}$ )

Show answer & explanation

Answer: 15

Answer

15

First, the rate is given as 20 feet per second. The total time must be converted entirely to seconds: 1 hour and 6 minutes equals 66 minutes. Multiplying 66 minutes by 60 seconds per minute gives 3,960 seconds. Next, use the formula Distance = Rate × Time to find the distance in feet: 20 × 3,960 = 79,200 feet. Finally, convert this distance into miles by dividing by 5,280. 79,200 ÷ 5,280 = 15 miles.

Step-by-Step Solution

1

Convert the total travel time into seconds to match the unit of the given speed.

The total time is 3,960 seconds.

Rates and times must share the same time unit before multiplying.

2

Calculate the total distance traveled in feet by multiplying the speed by the time in seconds.

The distance is 79,200 feet.

Distance equals rate multiplied by time (d = r * t).

3

Convert the distance from feet into miles by dividing by 5,280.

The final distance is 15 miles.

The question asks for the final answer in miles, and there are 5,280 feet in one mile.

Key Concept

Converting between multiple units of time and distance to solve for a missing variable in the distance formula.

Unit Conversions in Motion Problems

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Common Mistakes