Unit Rates Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB) — Page 2

Question 21Question →

An automated packaging system at a military supply center processes $4,500$ ration kits in $2.5$ hours. What is the unit rate of the system in ration kits per minute?

1,800

30

11,250

18

Show answer & explanation

Answer: 30

Answer

30

To find the unit rate in kits per minute, the time must first be converted from hours to minutes. Since there are

60

minutes in one hour,

2.5

hours is equivalent to

150

minutes (

2.5 \times 60 = 150

). Next, divide the total number of ration kits by the total number of minutes:

4,500 \div 150 = 30

. The system processes

30

ration kits per minute.

Step-by-Step Solution

1

Convert the total time from hours to minutes.

2.5 \text{ hours} \times 60 \text{ minutes/hour} = 150 \text{ minutes}

The question asks for the unit rate in kits per minute, so the given time must be in minutes.

2

Calculate the unit rate by dividing the total number of ration kits by the total time in minutes.

4,500 \div 150 = 30 \text{ kits per minute}

Unit rate is defined as the total quantity divided by the total time.

Key Concept

Unit Rates with Time Conversion

Question 22Question →

A medical logistics unit processes $3,600$ standard first-aid kits in $45$ minutes. What is the unit rate of processing in kits per hour?

4,800

80

8,000

480

Show answer & explanation

Answer: 4,800

Answer

The unit rate is 4,800 kits per hour.

To find the hourly unit rate, the processing time must be converted from minutes to hours, or the per-minute rate must be calculated and multiplied by 60. Processing

3,600

kits in

45

minutes equals

80

kits per minute. Multiplying by

60

minutes per hour gives the correct rate of

4,800

kits per hour.

Step-by-Step Solution

1

Convert the processing time from minutes to hours.

45 \text{ minutes} = \frac{45}{60} \text{ hours} = 0.75 \text{ hours}

The question asks for the unit rate in kits per hour, so the time unit must match the requested rate.

2

Divide the total number of kits by the time in hours to find the unit rate.

\frac{3,600}{0.75} = 4,800 \text{ kits per hour}

A unit rate represents the ratio of the total quantity to the total time.

Key Concept

Calculating unit rates with time conversions

Question 23Question →

A base quartermaster is evaluating the fuel efficiency of four different portable power generators. Match each generator's fuel consumption data to its correct unit rate in gallons per hour.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Generator W matches with

3.5

gallons per hour, Generator X matches with

3.75

gallons per hour, Generator Y matches with

6.5

gallons per hour, and Generator Z matches with

2.25

gallons per hour.

Each generator's fuel consumption is converted to an hourly rate by matching the time period into hours (e.g.,

2

days to

48

hours,

240

minutes to

4

hours) and then dividing the total gallons consumed by the total hours.

Step-by-Step Solution

1

Calculate the unit rate for Generator W.

14 \div 4 = 3.5

gallons per hour.

The rate is already given in hours, so divide the total gallons by the total hours.

2

Calculate the unit rate for Generator X by converting days to hours.

2

days =

48

hours.

180 \div 48 = 3.75

gallons per hour.

The unit rate must be in gallons per hour, so the time must first be converted from days to hours.

3

Calculate the unit rate for Generator Y.

26 \div 4 = 6.5

gallons per hour.

Divide the total volume of fuel by the given time in hours.

4

Calculate the unit rate for Generator Z by converting minutes to hours.

240

minutes =

4

hours.

9 \div 4 = 2.25

gallons per hour.

The unit rate must be in gallons per hour, so the time must first be converted from minutes to hours by dividing by

60

.

Key Concept

Calculating unit rates by ensuring equivalent units of measure before dividing the quantity by the time.

Question 24Question →

A supply depot crew loads $1,350$ cargo crates onto transport aircraft in $4.5$ hours. Assuming a constant work pace, how many crates does the crew load per minute?

3

50

300

5

Show answer & explanation

Answer: 5

Answer

5

The correct unit rate is found by first converting

4.5

hours to minutes. Since there are

60

minutes in an hour,

4.5 \times 60 = 270

minutes. Then, dividing the total quantity of

1,350

crates by the total time of

270

minutes yields exactly

5

crates per minute.

Step-by-Step Solution

1

Convert the total time from hours to minutes.

4.5 \text{ hours} \times 60 \text{ minutes/hour} = 270 \text{ minutes}

The question specifically asks for the unit rate in crates per minute, so the time must be in minutes.

2

Divide the total number of crates by the total time in minutes.

1,350 \text{ crates} \div 270 \text{ minutes} = 5 \text{ crates per minute}

The unit rate is found by dividing the total quantity by the total time.

Key Concept

Calculating unit rates requiring a preceding time unit conversion.

Question 25Question →

A quartermaster issues $1,050$ uniform shirts to new recruits over the course of a $3$ -hour and $30$ -minute processing block. Assuming a constant pace, what is the unit rate of shirts issued per minute?

Show answer & explanation

Answer: 5

Answer

The correct answer is 5 shirts per minute.

To find the unit rate in shirts per minute, the total time must first be converted entirely into minutes.

3

hours and

30

minutes is equal to

210

minutes. Dividing the total number of shirts (

1,050

) by the total number of minutes (

210

) results in exactly

5

shirts per minute.

Step-by-Step Solution

1

Convert the given time block into a single unit (minutes) to align with the question's requested rate.

3

hours and

30

minutes

= (3 \times 60) + 30 = 180 + 30 = 210

minutes.

The unit rate asked for is per minute, so the total time elapsed must be expressed in minutes.

2

Calculate the unit rate by dividing the total quantity by the total time in minutes.

1,050 \text{ shirts} \div 210 \text{ minutes} = 5 \text{ shirts per minute}

.

A unit rate compares a quantity to one unit of another quantity. Dividing the total items by the total minutes yields the number of items per single minute.

Key Concept

Calculating unit rates involving time conversion.

Question 26Question →

A military water purification unit has three filters operating at different unit rates. Filter X can purify $180$ gallons of water in $1.5$ hours. Filter Y can purify $320$ gallons in $2$ hours. Filter Z's purification rate is exactly $20\%$ faster than Filter X's rate. If all three filters are turned on at the same time, how many minutes will it take them to completely purify $1,484$ gallons of water?

Show answer & explanation

Answer: 210

Answer

210

The correct answer is found by first determining the individual hourly rates of each filter, adding them together for a combined rate, calculating the total hours required for the given volume, and finally converting that time into minutes.

Step-by-Step Solution

1

Calculate the unit rate for Filter X.

120

gallons per hour

To find the combined rate later, we first need the individual hourly rate of Filter X.

180 \div 1.5 = 120

.

2

Calculate the unit rate for Filter Y.

160

gallons per hour

We need the individual hourly rate of Filter Y to find the total combined rate.

320 \div 2 = 160

.

3

Calculate the unit rate for Filter Z.

144

gallons per hour

Filter Z operates

20\%

faster than Filter X, so its rate is

120 + (0.20 \times 120) = 144

.

4

Calculate the combined unit rate of all three filters.

424

gallons per hour

Since the filters operate simultaneously, their individual rates add together:

120 + 160 + 144 = 424

.

5

Determine the time in hours needed to purify

1,484

gallons.

3.5

hours

Time equals the total amount required divided by the combined rate:

1,484 \div 424 = 3.5

.

6

Convert the total time from hours to minutes.

210

minutes

The question explicitly asks for the answer in minutes.

3.5 \times 60 = 210

.

Key Concept

Calculating, modifying, and combining multiple unit rates, followed by a final unit conversion.

Alternative Method

You could convert the rates to gallons per minute immediately. Filter X is 2 gallons per minute, Filter Y is 2.67 gallons per minute, etc. However, this introduces repeating decimals early on, making the math significantly harder without a calculator. Keeping the rates in hours avoids complex fractions until the final step.

Estimated Time:3m 30s

Question 27Question →

A military transport truck travels $180$ miles on $20$ gallons of diesel fuel. A newer model travels $220$ miles on $22$ gallons of diesel fuel. The logistics team needs to select a truck for a supply route that is $360$ miles one-way. If the selected truck must complete a full round trip along this route, how many fewer gallons of diesel will the newer model use compared to the older model for the entire journey?

8

4

80

720

Show answer & explanation

Answer: 8

Answer

8

The correct answer is found by first calculating the unit rate for each truck: the older truck gets

9

mpg (

180 \div 20

) and the newer truck gets

10

mpg (

220 \div 22

). The total distance for a round trip is

720

miles (

360 \times 2

). For this journey, the older truck requires

80

gallons (

720 \div 9

) and the newer truck requires

72

gallons (

720 \div 10

). The difference is

8

gallons.

Step-by-Step Solution

1

Calculate the fuel efficiency (unit rate) for the older truck.

180 \div 20 = 9

miles per gallon (mpg).

Finding the unit rate allows us to calculate fuel consumption for any given distance.

2

Calculate the fuel efficiency for the newer model.

220 \div 22 = 10

miles per gallon (mpg).

This establishes the unit rate for the second vehicle.

3

Determine the total distance for the round trip.

360 \times 2 = 720

miles.

The route is

360

miles one-way, so a full round trip is double that distance.

4

Calculate the total fuel required for each truck for the round trip.

Older truck:

720 \div 9 = 80

gallons. Newer truck:

720 \div 10 = 72

gallons.

Divides the total distance by each truck's mpg to find the fuel needed.

5

Find the difference in fuel consumption.

80 - 72 = 8

gallons.

Subtracting the newer truck's fuel from the older truck's fuel gives the final savings.

Key Concept

Calculating and applying unit rates across multi-step word problems involving round trips.

Unit Rates

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Common Mistakes