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

Question 1Question →

A military logistics center uses two automated packaging machines to assemble field ration kits. Machine A can assemble $450$ kits in $1.5$ hours. Machine B can assemble $90$ kits every $15$ minutes. If both machines operate simultaneously at their respective constant rates, how many total ration kits can they assemble in $4$ hours?

2,640

1,224

1,560

165

Show answer & explanation

Answer: $2,640$

Answer

They can assemble

2,640

ration kits in

4

hours.

The correct answer is found by standardizing the production rates into hourly unit rates, adding them together, and multiplying by the total time. Machine A produces at

300

kits/hr (

450 \div 1.5

). Machine B produces at

360

kits/hr (

90 \times 4

, since

15

minutes is a quarter of an hour). The combined hourly rate is

660

kits/hr. In

4

hours, they produce

660 \times 4 = 2,640

kits.

Step-by-Step Solution

1

Calculate the hourly unit rate for Machine A.

450 \div 1.5 = 300

kits per hour.

To compare and combine rates, both machines must be evaluated using the same unit of time (hours).

2

Calculate the hourly unit rate for Machine B.

90

kits per

15

minutes is equal to

90 \times 4 = 360

kits per hour.

There are

60

minutes in an hour, which is exactly four

15

-minute segments (

60 \div 15 = 4

). Therefore, multiplying the

15

-minute production rate by

4

gives the hourly rate.

3

Calculate the combined hourly rate.

300 + 360 = 660

kits per hour.

Since both machines operate simultaneously, their individual hourly rates are added together to find the total combined rate.

4

Calculate the total kits assembled in

4

hours.

660 \times 4 = 2,640

kits.

Multiply the combined hourly unit rate by the total operating time to find the final production amount.

Key Concept

Unit Rates

Question 2Question →

Match each military logistical operation to its correct unit rate. Pay close attention to the requested units of measurement and necessary conversions.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: Supply truck with 12 miles per gallon, Drainage system with 60 gallons per minute, Packaging line with 420 rations per hour, and Generator with 12.5 milliliters per minute.

Each scenario requires identifying the total quantity of the numerator (miles, gallons, rations, milliliters) and dividing it by the corresponding total of the denominator (gallons, minutes, hours). In every case, this necessitates at least one preliminary conversion or calculation step.

Step-by-Step Solution

1

Calculate the fuel efficiency of the supply truck in miles per gallon.

Total distance =

45 \times 4 = 180

miles. Unit rate =

180 / 15 = 12

miles per gallon.

The fuel efficiency is found by dividing the total distance traveled by the total gallons of fuel consumed, requiring a preliminary distance calculation.

2

Calculate the pumping rate of the drainage system in gallons per minute.

Total time =

60 + 20 = 80

minutes. Unit rate =

4,800 / 80 = 60

gallons per minute.

The units requested are gallons per minute, so the total time must first be completely converted into minutes before dividing the volume.

3

Calculate the production rate of the packaging line in rations per hour.

Rate per minute =

315 / 45 = 7

rations/min. Rate per hour =

7 \times 60 = 420

rations per hour.

To find the hourly rate from a minute-based rate, first find the rate per minute, then scale it up by multiplying by the number of minutes in an hour (

60

).

4

Calculate the consumption rate of the generator in milliliters per minute.

Volume =

18 \times 1,000 = 18,000

mL. Time =

24 \times 60 = 1,440

minutes. Unit rate =

18,000 / 1,440 = 12.5

mL/min.

Both given quantities require unit conversions (liters to milliliters, and hours to minutes) before performing the final division to find the required rate.

Key Concept

Calculating unit rates involving multi-step operations and dimensional analysis (unit conversions).

Question 3Question →

An aviation maintenance depot uses two automated riveting machines to assemble fuselage panels. Machine A can install $240$ rivets in $4$ hours. Machine B can install $30$ rivets every $20$ minutes. If both machines operate simultaneously, how many hours will it take them to install a total of $6,300$ rivets?

30

42

63

70

Show answer & explanation

Answer: 42

Answer

The correct answer is 42 hours.

To solve this problem, both machine rates must first be converted to the same time unit (hours). Machine A operates at

60

rivets per hour (

240 \div 4

). Machine B operates at

90

rivets per hour (since there are three

20

-minute periods in an hour,

30 \times 3 = 90

). Together, they install

150

rivets per hour (

60 + 90

). Dividing the total requirement of

6,300

rivets by the combined rate of

150

rivets per hour yields exactly

42

hours.

Step-by-Step Solution

1

Calculate the unit rate for Machine A in rivets per hour.

240 \text{ rivets} \div 4 \text{ hours} = 60 \text{ rivets per hour}

To combine the rates of both machines, they must be in the same unit of measure (rivets per hour).

2

Calculate the unit rate for Machine B in rivets per hour.

30 \text{ rivets} \div 20 \text{ minutes} = 1.5 \text{ rivets per minute}

.

1.5 \times 60 = 90 \text{ rivets per hour}

Machine B's rate is given per

20

minutes, so it must be scaled up to an hourly rate by multiplying by

60

minutes.

3

Calculate the combined hourly rate of both machines.

60 + 90 = 150 \text{ rivets per hour}

The machines operate simultaneously, so their individual hourly rates are added together.

4

Determine the total time required to install

6,300

rivets.

6,300 \text{ rivets} \div 150 \text{ rivets per hour} = 42 \text{ hours}

Dividing the total work required by the combined hourly rate gives the total time needed.

Key Concept

Unit Rates and Multi-Step Rate Applications

Question 4Question →

A quartermaster purchases $2$ dozen identical tactical flashlights for a total cost of $\$720$ . What is the unit price of a single flashlight?

\$3

\$30

\$60

\$360

Show answer & explanation

Answer: $\$30$

Answer

The correct unit price is

\$30

per flashlight.

To find the unit price, the total cost must be divided by the total number of individual items. First, convert

2

dozen into a specific quantity by multiplying by

12

, yielding

24

flashlights. Then, divide the total cost of

\$720

by

24

, which equals

\$30

per flashlight.

Step-by-Step Solution

1

Determine the total number of flashlights purchased.

2 \text{ dozen} = 2 \times 12 = 24 \text{ flashlights}

You must know the exact number of individual items before you can calculate the cost of a single item.

2

Divide the total cost by the total number of items to find the unit price.

\$720 \div 24 = \$30

Unit price is found by dividing the total amount spent by the total quantity received.

Key Concept

Unit Price Calculation

Estimated Time:45s

Question 5Question →

A naval supply ship pumps $3,600$ gallons of fresh water into a destroyer's holding tanks over the course of $4$ hours. At what constant rate, in gallons per hour, is the water being pumped?

Show answer & explanation

Answer: 900

Answer

900

To find the rate in gallons per hour, the total number of gallons (

3,600

) is divided by the total number of hours (

4

), resulting in

900

gallons per hour.

Step-by-Step Solution

1

Identify the total quantity and the total time given in the scenario.

Total quantity =

3,600

gallons. Total time =

4

hours.

A unit rate requires knowing both the total amount and the corresponding time frame.

2

Divide the total gallons by the total hours to find the unit rate.

3,600 \div 4 = 900

Dividing the total amount by the number of hours yields the amount per single hour.

Key Concept

Calculating a basic unit rate by dividing a total quantity by a total time.

Question 6Question →

A military detail fills $300$ sandbags in $150$ minutes. What is the constant rate at which the detail fills the sandbags, in sandbags per hour?

120

2

12

0.5

Show answer & explanation

Answer: 120

Answer

120

The unit rate is found by first converting the time into hours (

150

minutes is

2.5

hours) and then dividing the total quantity (

300

sandbags) by this time, resulting in

120

sandbags per hour.

Step-by-Step Solution

1

Convert the total time from minutes to hours.

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

The requested unit rate is in sandbags per hour, so the time must be expressed in hours.

2

Calculate the unit rate by dividing the total number of sandbags by the total time in hours.

300 \text{ sandbags} \div 2.5 \text{ hours} = 120 \text{ sandbags per hour}

A unit rate represents the quantity produced per single unit of time.

Key Concept

Calculating unit rates with time conversion

Question 7Question →

Match each military vehicle's travel scenario to its correct average unit rate in miles per hour.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The jeep matches to 40 mph, the helicopter to 150 mph, the truck to 55 mph, and the patrol boat to 36 mph.

Each unit rate is found by applying the formula for speed: Speed = Distance ÷ Time. Calculating this for each vehicle yields the correct matching pairs.

Step-by-Step Solution

1

Calculate the unit rate for the jeep.

120 / 3 = 40 miles per hour

To find the average speed, divide total distance by total time.

2

Calculate the unit rate for the helicopter.

300 / 2 = 150 miles per hour

To find the average speed, divide total distance by total time.

3

Calculate the unit rate for the supply truck.

220 / 4 = 55 miles per hour

To find the average speed, divide total distance by total time.

4

Calculate the unit rate for the patrol boat.

180 / 5 = 36 miles per hour

To find the average speed, divide total distance by total time.

Key Concept

A unit rate compares a quantity to one unit of another quantity, often calculated by dividing the total amount by the total time or number of items.

Question 8Question →

A civilian contractor works $5$ days a week for $8$ hours each day on a military base. If the contractor earns $\$840$ for the entire week, what is the contractor's hourly wage?

\$21

\$105

\$168

\$210

Show answer & explanation

Answer: \$21

Answer

The contractor's hourly wage is

\$21

.

The total number of hours worked in the week is found by multiplying the

5

days by

8

hours per day, which equals

40

hours. The hourly wage is then calculated by dividing the total weekly earnings by the total hours worked:

\$840 \div 40 = \$21

per hour.

Step-by-Step Solution

1

Calculate the total number of hours the contractor works in the week.

5 \text{ days} \times 8 \text{ hours/day} = 40 \text{ hours}

To find the hourly wage, the total earnings must be divided by the total hours worked.

2

Divide the total weekly earnings by the total hours worked to find the hourly wage.

\$840 \div 40 \text{ hours} = \$21 \text{ per hour}

The unit rate (hourly wage) is the ratio of total pay to total time.

Key Concept

Calculating a unit rate by determining the total quantity (hours) and dividing the total amount (earnings) by that quantity.

Question 9Question →

A warehouse forklift moves $84$ cargo pallets in $6$ hours. At this constant rate, how many pallets does the forklift move per hour?

Show answer & explanation

Answer: 14

Answer

The forklift moves

14

pallets per hour.

To determine the unit rate, divide the total quantity (

84

pallets) by the total elapsed time (

6

hours). The result is a constant rate of

14

pallets per hour.

Step-by-Step Solution

1

Identify the total quantity of items and the total time.

Total pallets =

84

, Total time =

6

hours.

These are the two values needed to set up the unit rate calculation.

2

Divide the total pallets by the total hours.

84 \div 6 = 14

The unit rate 'pallets per hour' requires dividing the number of pallets by the number of hours.

Key Concept

Calculating unit rates

Estimated Time:45s

Question 10Question →

A mess hall crew prepares $240$ field rations in $120$ minutes. What is the crew's constant preparation rate in rations per hour?

2

12

120

480

Show answer & explanation

Answer: 120

Answer

120

The rate is found by first converting

120

minutes into

2

hours, then dividing the

240

rations by

2

hours to obtain

120

rations per hour.

Step-by-Step Solution

1

Convert the given time from minutes to hours.

120 \text{ minutes} = 2 \text{ hours}

The question asks for the rate in rations per hour, so the time unit must be in hours.

2

Divide the total number of rations by the total time in hours.

240 \div 2 = 120

Dividing the total quantity by the total time calculates the unit rate.

Key Concept

Calculating a unit rate often requires first converting time into the requested units before performing division.

Question 11Question →

A logistics officer is reviewing purchase orders for safety equipment. Match each bulk purchase scenario to its correct unit price.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct pairings are determined by dividing the total cost by the quantity for each scenario, yielding the unit rates of

5,

3,

6, and

4 respectively.

Each correct match is found by identifying the unit price using the formula: Total Cost ÷ Quantity.

Step-by-Step Solution

1

Calculate the unit price for the protective goggles.

60 / 12 =

5 per pair.

Unit price is total cost divided by quantity.

2

Calculate the unit price for the work gloves.

90 / 30 =

3 per pair.

Unit price is total cost divided by quantity.

3

Calculate the unit price for the heavy-duty flashlights.

48 / 8 =

6 per flashlight.

Unit price is total cost divided by quantity.

4

Calculate the unit price for the high-visibility vests.

100 / 25 =

4 per vest.

Unit price is total cost divided by quantity.

Key Concept

Calculating unit rates by dividing the total amount by the number of units.

Question 12Question →

An operations chief needs to verify the hourly fuel consumption for a deployed mechanized unit. Match each asset's usage report to its calculated unit rate in gallons per hour.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Combat engineer vehicle matches to 25 gallons per hour; Utility helicopter matches to 80 gallons per hour; Tactical field generator matches to 15 gallons per hour; Cargo transport truck matches to 12 gallons per hour.

Each asset's fuel consumption rate is found by setting up a ratio of total gallons used to total hours operated, and then dividing to find the amount for exactly one hour. Any time given in minutes must be converted to hours to match the requested unit of 'gallons per hour'.

Step-by-Step Solution

1

Calculate the unit rate for the combat engineer vehicle.

350 \div 14 = 25

gallons per hour.

Unit rate is found by dividing the total quantity (gallons) by the total time (hours).

2

Calculate the unit rate for the utility helicopter.

90

minutes is

1.5

hours.

120 \div 1.5 = 80

gallons per hour.

The rate requested is in gallons per hour, so minutes must first be converted to hours before dividing.

3

Calculate the unit rate for the tactical field generator.

45 \div 3 = 15

gallons per hour.

Unit rate is found by dividing the total quantity (gallons) by the total time (hours).

4

Calculate the unit rate for the cargo transport truck.

144 \div 12 = 12

gallons per hour.

Unit rate is found by dividing the total quantity (gallons) by the total time (hours).

Key Concept

Calculating unit rates by dividing a total quantity by a total elapsed time, ensuring units align correctly.

Question 13Question →

A refueling tanker transfers $450$ gallons of aviation fuel into an aircraft in $15$ minutes. What is the tanker's transfer rate in gallons per hour?

1,800

3,000

112.5

30

Show answer & explanation

Answer: $1,800$

Answer

The correct answer is

1,800

.

The correct transfer rate is found by determining how much fuel is pumped in one minute, which is

450 \div 15 = 30

gallons per minute. Since there are

60

minutes in an hour, multiply this rate by

60

to get

1,800

gallons per hour.

Step-by-Step Solution

1

Find the unit rate in gallons per minute.

450 \div 15 = 30

gallons per minute.

This establishes the base rate of fuel transfer before scaling up to an hourly rate.

2

Convert the per-minute rate to a per-hour rate.

30 \times 60 = 1,800

gallons per hour.

There are 60 minutes in an hour, so the minute rate must be multiplied by 60 to find the hourly rate.

Key Concept

Calculating unit rates and applying time conversions.

Estimated Time:1m 0s

Question 14Question →

A tactical communications array transmits $1,800$ megabytes of encrypted data in $4.5$ minutes. At this constant rate, how many megabytes of data does the array transmit in $18$ seconds?

Show answer & explanation

Answer: 120

Answer

120

The correct answer is derived by first establishing the transmission rate of

400

megabytes per minute (

1,800 \div 4.5

). Since the required timeframe is given in seconds, it must be converted to minutes (

18 \div 60 = 0.3

minutes). Multiplying the rate by the converted time gives

120

megabytes.

Step-by-Step Solution

1

Calculate the unit transmission rate in megabytes per minute.

1,800 \div 4.5 = 400

megabytes per minute

Finding the rate per minute allows for scaling the transmission amount to any other duration.

2

Convert the target time from seconds to minutes.

18 \div 60 = 0.3

minutes

The established unit rate is in minutes, so the target time must match this temporal unit before multiplying.

3

Multiply the unit rate by the converted target time.

400 \times 0.3 = 120

megabytes

Multiplying the rate (megabytes per minute) by the time (minutes) yields the total amount of data transmitted.

Key Concept

Calculating unit rates and applying time unit conversions (seconds to minutes) to solve for a specific quantity.

Question 15Question →

A military textile facility produces $1,200$ combat uniform shirts over a standard $5$ -day workweek. If the facility operates for a single $8$ -hour shift each day, what is the facility's production rate in shirts per hour?

30

150

240

300

Show answer & explanation

Answer: $30$

Answer

The facility's production rate is

30

shirts per hour.

To find the hourly production rate, first determine the total hours worked by multiplying the number of days by the hours per shift (

5 \text{ days} \times 8 \text{ hours} = 40 \text{ hours}

). Then, divide the total production by the total hours (

1,200 \text{ shirts} \div 40 \text{ hours} = 30 \text{ shirts per hour}

).

Step-by-Step Solution

1

Calculate the total number of hours the facility operated.

5 \text{ days} \times 8 \text{ hours/day} = 40 \text{ hours}

To find the hourly rate, the total time must be expressed in hours.

2

Divide the total number of shirts produced by the total number of hours.

1,200 \div 40 = 30 \text{ shirts per hour}

Dividing total quantity by total time yields the unit rate.

Key Concept

Unit Rates and Time Conversions

Question 16Question →

A shipyard damage control team is evaluating four auxiliary water pumps. Match each pump's performance test results to its calculated unit rate in gallons per minute (GPM).

Click a left item, then click its matching right item

Show answer & explanation

Answer

Pump Alpha matches

150

GPM, Pump Bravo matches

140

GPM, Pump Charlie matches

160

GPM, and Pump Delta matches

170

GPM.

Each pump's unit rate is determined by dividing the total gallons removed by the total number of minutes. This yields the uniform rate in gallons per minute (GPM).

Step-by-Step Solution

1

Calculate the unit rate for Pump Alpha.

1,800 \div 12 = 150

gallons per minute.

Dividing the total volume by the total time gives the unit rate.

2

Calculate the unit rate for Pump Bravo.

3,500 \div 25 = 140

gallons per minute.

Dividing the total volume by the total time gives the unit rate.

3

Calculate the unit rate for Pump Charlie.

4,800 \div 30 = 160

gallons per minute.

Dividing the total volume by the total time gives the unit rate.

4

Calculate the unit rate for Pump Delta.

6,800 \div 40 = 170

gallons per minute.

Dividing the total volume by the total time gives the unit rate.

Key Concept

Calculating unit rates by dividing a total quantity by the elapsed time to find the amount per single unit of time.

Question 17Question →

A combat engineer battalion is clearing debris from a damaged supply route. They are able to clear $1,800$ square feet of the route in $45$ minutes. Operating at this constant rate, what is the battalion's clearance rate in square feet per hour?

40

1,350

2,400

4,000

Show answer & explanation

Answer: $2,400$

Answer

The correct clearance rate is

2,400

square feet per hour.

To find the hourly clearance rate, we can first determine the rate per minute:

1,800

square feet divided by

45

minutes gives

40

square feet per minute. Since there are

60

minutes in an hour, we multiply

40

by

60

to get

2,400

square feet per hour. Alternatively,

45

minutes is

0.75

hours, and

1,800 \div 0.75 = 2,400

.

Step-by-Step Solution

1

Find the unit rate per minute by dividing the total area cleared by the total minutes.

1,800 \div 45 = 40

square feet per minute

This establishes the base clearance rate in the provided time unit.

2

Convert the per-minute rate to a per-hour rate by multiplying by

60

.

40 \times 60 = 2,400

square feet per hour

There are

60

minutes in one hour, so multiplying the minute rate by

60

gives the hourly rate.

Key Concept

Calculating unit rates and performing necessary unit conversions.

Estimated Time:1m 0s

Question 18Question →

A field kitchen consumes $15$ pounds of coffee over a $4$ -hour breakfast service. What is the unit rate of coffee consumption, in ounces per hour?

Show answer & explanation

Answer: 60

Answer

60

The unit rate is found by first converting the total weight into the requested units. Since 1 pound equals 16 ounces, 15 pounds is equal to 240 ounces. Dividing this 240 ounces by the 4 hours of service gives the correct unit rate of 60 ounces per hour.

Step-by-Step Solution

1

Convert the total coffee weight from pounds to ounces.

15 \times 16 = 240

ounces

The question specifically asks for the rate in ounces per hour, and there are 16 ounces in 1 pound.

2

Calculate the unit rate by dividing the total ounces by the total hours.

240 \div 4 = 60

ounces per hour

A unit rate represents the quantity of one variable per single unit of another variable, found here by dividing total consumption by total time.

Key Concept

Calculating Unit Rates with Unit Conversions

Question 19Question →

A mobile water purification system can process $5,400$ gallons of water in $1.5$ hours. What is the unit rate of water processed, in gallons per minute?

36

60

600

3,600

Show answer & explanation

Answer: 60

Answer

The correct unit rate is 60 gallons per minute.

The correct answer is found by first converting

1.5

hours to minutes (

1.5 \times 60 = 90

minutes). Then, divide the total gallons by the total minutes to find the rate:

5,400 \div 90 = 60

gallons per minute.

Step-by-Step Solution

1

Convert the given time from hours to minutes.

1.5 \text{ hours} \times 60 \text{ minutes/hour} = 90 \text{ minutes}

.

The question specifically asks for the unit rate in gallons per minute, so the time measurement must match.

2

Divide the total amount of water by the total number of minutes to find the unit rate.

5,400 \text{ gallons} \div 90 \text{ minutes} = 60 \text{ gallons per minute}

.

A unit rate represents the quantity of one variable for every single unit of another variable.

Key Concept

Calculating unit rates involving time conversions

Estimated Time:1m 0s

Question 20Question →

A logistics command is tracking the movement of four supply convoys traveling along different routes. Match each convoy's travel data to its correct average unit rate in miles per hour (mph).

Click a left item, then click its matching right item

Show answer & explanation

Answer

Alpha Convoy travels at 45 mph, Bravo Convoy at 48 mph, Charlie Convoy at 52 mph, and Delta Convoy at 50 mph.

Each convoy's speed is found by dividing the total miles traveled by the total hours elapsed, carefully converting any minute values into fractional or decimal hours first.

Step-by-Step Solution

1

Calculate the unit rate for Alpha Convoy.

45

mph

The time is given in minutes, so it must be converted to hours.

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

. Then,

15 \div \frac{1}{3} = 45

mph.

2

Calculate the unit rate for Bravo Convoy.

48

mph

The time is already in hours. Simply divide distance by time:

96 \div 2 = 48

mph.

3

Calculate the unit rate for Charlie Convoy.

52

mph

The time is in hours as a decimal. Divide distance by time:

130 \div 2.5 = 52

mph.

4

Calculate the unit rate for Delta Convoy.

50

mph

Convert minutes to hours:

42 \text{ minutes} = \frac{42}{60} \text{ hours} = 0.7 \text{ hours}

. Divide distance by time:

35 \div 0.7 = 50

mph.

Key Concept

Calculating unit rates (speed) by dividing distance by time, requiring unit conversion when time is given in minutes.

Estimated Time:2m 0s

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