Measurement and Unit Conversions Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

A specialized water purification system takes $3$ hours and $20$ minutes to process one complete cycle. If an engineering detachment runs the system continuously for exactly $2.5$ days, how many complete cycles will the system finish?

Show answer & explanation

Answer: 18

Answer

18

The correct answer is found by establishing a common unit of time (minutes) for both the total duration and the cycle length. First, converting the

2.5

days of total operation into hours gives

60

hours, which equals

3600

minutes. Next, converting the

3

hour and

20

minute cycle duration into minutes yields

200

minutes. Finally, dividing the total available time (

3600

minutes) by the cycle time (

200

minutes) results in exactly

18

complete cycles.

Step-by-Step Solution

1

Convert the total continuous running time from days to hours.

2.5 \times 24 = 60

hours

To establish a smaller standard unit of time to match the cycle duration.

2

Convert the total operating hours into minutes.

60 \times 60 = 3600

minutes

Minutes will serve as the common baseline unit for the calculation.

3

Convert the required time for a single cycle into minutes.

3 \times 60 = 180

minutes;

180 + 20 = 200

minutes

To express the cycle duration in the exact same unit as the total running time.

4

Calculate the total number of completed cycles by dividing the total minutes by the cycle minutes.

3600 \div 200 = 18

cycles

This division determines how many

200

-minute intervals fit within the

3600

-minute window.

Key Concept

Multi-step time unit conversions and calculating work rate.

Question 2Question →

A shipment of medical supplies weighs $44 \text{ pounds}$ . If $1 \text{ kilogram}$ is approximately equal to $2.2 \text{ pounds}$ , what is the weight of the shipment in kilograms?

0.05

2

20

96.8

Show answer & explanation

Answer: 20

Answer

20

To convert a weight from pounds to kilograms given that 1 kilogram equals 2.2 pounds, you must divide the total pounds by 2.2. Setting up the equation: 44 / 2.2 yields exactly 20. Thus, the shipment weighs 20 kilograms.

Step-by-Step Solution

1

Identify the given value and the unit conversion factor.

Given weight: 44 pounds. Conversion factor: 1 kilogram = 2.2 pounds.

This establishes the mathematical relationship needed to convert the weight from the US customary system to the metric system.

2

Set up the appropriate calculation to convert pounds to kilograms.

Divide 44 by 2.2 (44 / 2.2).

Since 1 kilogram is heavier than 1 pound (it equals 2.2 pounds), there will be fewer kilograms than pounds. Therefore, division is the correct operation.

3

Perform the division.

44 / 2.2 = 20.

To divide by a decimal, shift the decimal point one place to the right for both numbers, making it 440 / 22, which exactly equals 20.

Key Concept

Converting between US customary and metric weight units using division.

Alternative Method

You can set up a formal proportion: 1 kg / 2.2 lbs = x kg / 44 lbs. Cross-multiply to get 2.2x = 44, then solve for x by dividing both sides by 2.2.

Estimated Time:45s

Question 3Question →

A landscape architect is reviewing a scale drawing of a rectangular park. On the drawing, the scale is indicated as $\frac{2}{3}$ inch = $12$ yards. The perimeter of the park on the drawing is $14$ inches, and its length is $4\frac{1}{2}$ inches. What is the actual width of the park in feet?

15

45

60

135

Show answer & explanation

Answer: 135

Answer

135

To find the correct answer, three phases are required. First, use the perimeter formula (

P = 2L + 2W

) to find the drawing width:

14 = 2(4.5) + 2W \rightarrow W = 2.5

inches. Next, find the unit scale by dividing

12

yards by

\frac{2}{3}

inch, yielding

18

yards per inch. Multiplying the

2.5

-inch drawing width by

18

gives an actual width of

45

yards. Finally, convert yards to feet by multiplying by

3

, resulting in

135

feet.

Step-by-Step Solution

1

Determine the width of the park on the scale drawing.

The width on the drawing is

2.5

inches.

The formula for the perimeter of a rectangle is

P = 2L + 2W

. Substituting the given values,

14 = 2(4\frac{1}{2}) + 2W

, which simplifies to

14 = 9 + 2W

. Solving for

W

gives

2W = 5

, so

W = 2.5

.

2

Calculate the unit scale rate.

1

inch on the drawing represents

18

yards in reality.

To find the value of

1

inch, divide the actual distance by the drawing distance:

12 \div \frac{2}{3} = 12 \times \frac{3}{2} = 18

yards per inch.

3

Calculate the actual width of the park in yards.

The actual width is

45

yards.

Multiply the drawing width by the unit scale rate: $2.5 \text{ inches} \times 18 \text{ yards/inch} = 45 \text{ yards}.

4

Convert the actual width from yards to feet.

The final actual width is

135

feet.

There are

3

feet in

1

yard. Multiply the width in yards by

3

:

45 \times 3 = 135

feet.

Key Concept

Combining geometric perimeter calculations with multi-step scale and unit conversions.

Estimated Time:3m 0s

Question 4Question →

A logistics officer must load four distinct cargo items onto a transport aircraft. To maintain proper weight distribution, the items must be loaded in a specific sequence based on their total weight. Arrange the following cargo items in order from lightest to heaviest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from lightest to heaviest is: the crate (

2,250

lbs), the pallet (

2,280

lbs), the container (

2,300

lbs), and the supply pod (

2,330

lbs).

By converting all items to a common unit (pounds), we can accurately compare their weights: the crate is

2,250

lbs, the pallet is

2,280

lbs, the container is

2,300

lbs, and the supply pod is

2,330

lbs. Arranging these from lightest to heaviest yields the correct sequence.

Step-by-Step Solution

1

Convert the weight of the crate to pounds.

2,250

lbs

Standardizing all weights to a single unit (pounds) allows for direct comparison.

\frac{9}{8} \times 2,000 = 2,250

.

2

Convert the weight of the pallet to pounds.

2,280

lbs

Since there are

16

ounces in a pound, divide by

16

.

36,480 \div 16 = 2,280

.

3

Convert the weight of the container to pounds.

2,300

lbs

Since there are

2,000

pounds in a ton, multiply by

2,000

.

1.15 \times 2,000 = 2,300

.

4

Convert the weight of the supply pod to pounds.

2,330

lbs

The pod has mixed units. Convert the ton to

2,000

pounds and the ounces to pounds (

5,280 \div 16 = 330

). Adding them gives

2,000 + 330 = 2,330

.

5

Arrange the converted weights in ascending order.

2,250 < 2,280 < 2,300 < 2,330

The question asks for the items to be ordered from lightest to heaviest.

Key Concept

Multi-step conversion between ounces, pounds, and tons.

Estimated Time:3m 0s

Question 5Question →

A military training exercise lasts for exactly 2 hours and 45 minutes. What is the total duration of the exercise in minutes?

Show answer & explanation

Answer: 165

Answer

165

The correct total is found by converting the 2 hours into 120 minutes and adding the extra 45 minutes, resulting in a total of 165 minutes.

Step-by-Step Solution

1

Convert the hours portion of the duration to minutes.

2 hours × 60 minutes/hour = 120 minutes.

Time is based on a base-60 system, meaning each hour contains exactly 60 minutes.

2

Add the remaining minutes to the converted hour total.

120 minutes + 45 minutes = 165 minutes.

To find the total duration in a single unit, all partial time units must be combined.

Key Concept

Converting mixed time units (hours and minutes) into a single unit (minutes).

Question 6Question →

A surveillance drone has a maximum flight endurance of 345 minutes before its battery is completely depleted. If the drone is launched at 21:40 for a continuous mission, at what time will the drone's battery be completely depleted?

01:25

03:15

03:25

03:55

Show answer & explanation

Answer: 03:25

Answer

03:25

To find the completion time, you must add the total duration to the start time. First, convert 345 minutes into hours and minutes by dividing by 60, which gives 5 hours with a remainder of 45 minutes. Next, add 5 hours and 45 minutes to the launch time of 21:40. Adding the hours gives 26:40. Adding the 45 minutes gives 26:85. Since 85 minutes is equivalent to 1 hour and 25 minutes, this shifts the time to 27:25. Finally, subtract 24:00 to account for crossing midnight, resulting in the correct time of 03:25.

Step-by-Step Solution

1

Convert the total flight duration from minutes to hours and minutes.

345 minutes ÷ 60 = 5 hours with a remainder of 45 minutes.

Converting to hours and minutes makes it easier to add to the given start time.

2

Add the flight hours to the launch time.

21:40 + 5 hours = 26:40.

This finds the hour of completion before adjusting for the 24-hour clock.

3

Add the remaining flight minutes to the result from Step 2.

26:40 + 45 minutes = 26:85.

This incorporates the remaining minutes of the flight time.

4

Format the resulting time into a standard 24-hour clock format.

26:85 becomes 27:25 (since 85 minutes is 1 hour and 25 minutes). 27:25 on a 24-hour clock is calculated as 27:25 - 24:00 = 03:25.

Time must be expressed in a standard 24-hour format, properly accounting for crossing midnight (24:00).

Key Concept

Converting minutes into hours and minutes, and accurately adding elapsed time across the midnight boundary on a 24-hour clock.

Question 7Question →

The motor pool needs to prepare a specialized antifreeze mixture for 56 tactical vehicles. Each vehicle requires exactly 3.5 gallons of the final mixture. The required mixture consists of 3 parts concentrated coolant to 4 parts distilled water by volume. The motor pool currently has 20 gallons, 1 quart, and 1 pint of concentrated coolant in inventory. How many additional pints of concentrated coolant must be requisitioned to complete the maintenance on all vehicles?

509

512

733

1013

Show answer & explanation

Answer: 509

Answer

509

The correct answer accurately calculates the total final mixture as 196 gallons (56 * 3.5). Using the 3:4 ratio, the coolant represents 3/7 of the total, meaning 84 gallons of coolant are needed. Converting 84 gallons to pints gives 672 pints. The inventory of 20 gallons, 1 quart, and 1 pint equals exactly 163 pints (160 + 2 + 1). Subtracting the 163 pints in inventory from the 672 pints needed leaves a deficit of 509 pints.

Step-by-Step Solution

1

Calculate the total volume of the final mixture required for all vehicles.

56 vehicles * 3.5 gallons/vehicle = 196 gallons of final mixture.

Determines the total capacity needed before finding the specific amount of concentrated coolant.

2

Determine the volume of concentrated coolant needed.

196 gallons * (3 parts coolant / 7 total parts) = 84 gallons of concentrated coolant.

Applies the part-to-whole ratio (3 parts coolant + 4 parts water = 7 total parts) to find the coolant portion.

3

Convert the required amount of coolant into pints.

84 gallons * 8 pints/gallon = 672 pints.

Prepares the required amount in the target unit (pints) requested by the question. (1 gallon = 4 quarts, 1 quart = 2 pints).

4

Convert the current inventory of coolant into pints.

(20 gallons * 8) + (1 quart * 2) + 1 pint = 160 + 2 + 1 = 163 pints.

Standardizes the inventory volume to pints so it can be subtracted from the total required.

5

Subtract the inventory from the total needed to find the additional amount required.

672 pints - 163 pints = 509 pints.

Finds the exact deficit that must be requisitioned.

Key Concept

US Customary Capacity and Volume Conversions with Ratios

Question 8Question →

A logistics team is given a time frame of exactly $4.5$ hours to fully load a supply plane. What is the total duration of this time frame expressed in minutes?

270

290

245

450

Show answer & explanation

Answer: 270

Answer

The total duration of the time frame is 270 minutes.

The correct answer is found by multiplying the total number of hours (

4.5

) by the number of minutes in a single hour (

60

).

4.5 \times 60 = 270

minutes.

Step-by-Step Solution

1

Identify the conversion factor between hours and minutes.

1

hour

= 60

minutes.

To convert a measurement in hours to minutes, you must multiply by 60.

2

Set up the multiplication for the total hours given.

4.5 \times 60

The team has 4.5 hours, and each hour contains 60 minutes.

3

Calculate the final product.

4.5 \times 60 = 270

minutes.

This can also be calculated by splitting the time:

4

hours

\times 60 = 240

minutes, and

0.5

hours (half an hour) is

30

minutes.

240 + 30 = 270

minutes.

Key Concept

Time Conversion

Question 9Question →

A motor pool mechanic is reviewing the scheduled time required for four different vehicle maintenance tasks. Arrange the given task durations from the shortest amount of time to the longest amount of time.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct sequence from shortest to longest is:

1

hour and

15

minutes (

75

minutes),

85

minutes,

1.5

hours (

90

minutes), and finally

100

minutes.

By converting all the task durations into minutes, we get

75

minutes,

85

minutes,

90

minutes, and

100

minutes. Ordering these values mathematically from smallest to largest yields the correct chronological sequence.

Step-by-Step Solution

1

Convert all the given time durations into a single common unit, such as minutes.

1

hour and

15

minutes =

75

minutes;

85

minutes =

85

minutes;

1.5

hours =

90

minutes;

100

minutes =

100

minutes.

Comparing measurements is much easier and more accurate when every value is expressed in the exact same unit.

2

Order the newly converted values mathematically from the smallest number to the largest number.

75 < 85 < 90 < 100

The question specifically asks for the durations to be arranged from the shortest amount of time to the longest.

3

Match the ordered numerical values back to their original given text formats.

1

hour and

15

minutes, then

85

minutes, then

1.5

hours, then

100

minutes.

This establishes the final correct arrangement of the provided items.

Key Concept

Converting mixed time units (hours and minutes) and decimal hours into a single unit (minutes) to accurately compare and order durations.

Question 10Question →

A logistics supply convoy has a strict operational window of $72$ hours to complete its route. The first leg of the journey takes $1$ day, $9$ hours, and $45$ minutes. The second leg takes $830$ minutes. Before the final leg, the crew takes a mandatory rest period of $4.5$ hours. How many minutes remain in the $72$ -hour operational window for the convoy to complete the final leg?

Show answer & explanation

Answer: 1195

Answer

1195

The total operational window is

4,320

minutes (

72 \times 60

). The elapsed time includes

2,025

minutes for leg 1 (

33 \times 60 + 45

),

830

minutes for leg 2, and

270

minutes for rest (

4.5 \times 60

). The sum of these elapsed times is

3,125

minutes. Subtracting the total elapsed time from the total available window leaves exactly

1,195

minutes.

Step-by-Step Solution

1

Calculate total available time in minutes.

4,320

minutes

Converting the

72

-hour window to a smaller, standard unit (minutes) makes the final subtraction easier.

2

Convert the duration of the first leg entirely into minutes.

2,025

minutes

The first leg is mixed units (

1

day,

9

hours,

45

minutes).

1

day =

24

hours, plus

9

hours =

33

hours.

33 \times 60 = 1,980

minutes, plus

45

minutes =

2,025

minutes.

3

Convert the rest period into minutes.

270

minutes

4.5

hours requires conversion.

4.5 \times 60 = 270

minutes.

4

Calculate the total time elapsed.

3,125

minutes

Sum the durations:

2,025

(leg 1) +

830

(leg 2) +

270

(rest) =

3,125

minutes used.

5

Subtract the elapsed time from the total window.

1,195

minutes

4,320 - 3,125 = 1,195

minutes remaining for the final leg.

Key Concept

Converting mixed time units (days, hours, minutes, and fractional hours) into a single base unit to calculate remaining elapsed time.

Estimated Time:2m 30s

Question 11Question →

A topographic map uses a scale of $\frac{3}{8}\text{ inch} = 15\text{ miles}$ . A rectangular section of a national forest is shown on this map with dimensions of $1\frac{1}{2}\text{ inches}$ by $2\frac{1}{4}\text{ inches}$ . If a conservation program plans to plant $400$ trees per square mile throughout this entire section, how many thousands of trees will be planted in total?

Show answer & explanation

Answer: 2160

Answer

2160

The correct answer is found by first determining the unit scale factor. Since 3/8 inch represents 15 miles, dividing 15 by 3/8 reveals that 1 inch represents 40 miles. Multiplying the map dimensions (1.5 inches and 2.25 inches) by 40 gives the actual dimensions of 60 miles and 90 miles. The actual area is the product of these dimensions, or 5,400 square miles. Multiplying the area by 400 trees per square mile yields 2,160,000 total trees. Finally, dividing by 1,000 gives the answer in thousands: 2,160.

Step-by-Step Solution

1

Calculate the unit scale (miles per inch).

\frac{3}{8}\text{ inch} = 15\text{ miles} \Rightarrow 1\text{ inch} = 15 \times \frac{8}{3} = 40\text{ miles}

.

Finding the value of 1 inch makes it much easier to convert the mixed-fraction map dimensions.

2

Convert the map width to actual miles.

1\frac{1}{2}\text{ inches} = 1.5 \times 40 = 60\text{ miles}

.

The linear scale applies directly to one-dimensional measurements.

3

Convert the map length to actual miles.

2\frac{1}{4}\text{ inches} = 2.25 \times 40 = 90\text{ miles}

.

Applying the same linear scale factor to the other dimension.

4

Calculate the actual area of the forest.

60\text{ miles} \times 90\text{ miles} = 5400\text{ square miles}

.

The total planting area is required to determine how many trees are needed.

5

Calculate the total number of trees.

5400\text{ square miles} \times 400\text{ trees/square mile} = 2,160,000\text{ trees}

.

Applying the rate of 400 trees per square mile yields the absolute total.

6

Convert the final answer to the requested unit (thousands).

2,160,000 \div 1000 = 2160\text{ thousands}

.

The question specifically asks 'how many thousands of trees'.

Key Concept

Converting mixed-fraction map scales into actual dimensions to calculate applied area.

Question 12Question →

A construction crew has a spool containing exactly $\frac{1}{4}$ mile of underground cable. They use $120 \frac{2}{3}$ yards of the cable for their first trench and $412$ feet $8$ inches of the cable for their second trench. How much cable remains on the spool?

545 feet 4 inches

450 feet

786 feet 8 inches

545 feet 2 inches

Show answer & explanation

Answer: 545 feet 4 inches

Answer

545 feet 4 inches

To find the remaining cable, all measurements must be converted to a common unit. First, find the total cable in feet: since

1 \text{ mile} = 5280 \text{ feet}

,

\frac{1}{4} \text{ mile} = 1320 \text{ feet}

. Next, convert the first trench length to feet:

120 \frac{2}{3} \text{ yards} \times 3 \text{ feet/yard} = 362 \text{ feet}

. The second trench is

412 \text{ feet } 8 \text{ inches}

. The total used is

362 \text{ feet} + 412 \text{ feet } 8 \text{ inches} = 774 \text{ feet } 8 \text{ inches}

. Finally, subtract this from the starting amount. Borrowing

1 \text{ foot}

(

12 \text{ inches}

) from

1320 \text{ feet}

gives

1319 \text{ feet } 12 \text{ inches}

. Subtracting the used cable gives

1319 - 774 = 545 \text{ feet}

and

12 - 8 = 4 \text{ inches}

.

Step-by-Step Solution

1

Convert the total cable length from miles to feet.

\frac{1}{4} \times 5280 = 1320

feet.

Standardizing all measurements to the same base unit (feet) is required before adding or subtracting.

2

Convert the length used for the first trench from yards to feet.

120 \frac{2}{3} \times 3 = 362

feet.

There are 3 feet in a yard, so multiplying the mixed fraction by 3 gives the exact length in feet.

3

Calculate the total amount of cable used for both trenches.

362 \text{ feet} + 412 \text{ feet } 8 \text{ inches} = 774 \text{ feet } 8 \text{ inches}

.

Adding the individual segments provides the total length that must be subtracted from the spool.

4

Subtract the total used cable from the total spool length.

1320 \text{ feet} - 774 \text{ feet } 8 \text{ inches} = 545 \text{ feet } 4 \text{ inches}

.

To subtract the 8 inches, borrow 1 foot (12 inches) from 1320 feet to make it 1319 feet 12 inches. Subtracting yields

1319 - 774 = 545

feet and

12 - 8 = 4

inches.

Key Concept

Multi-step conversion and arithmetic using US Customary linear measurements

Question 13Question →

A base security system requires a full diagnostic scan that takes exactly $3.4$ hours to complete. What is the total duration of this diagnostic scan in minutes?

204

220

340

2040

Show answer & explanation

Answer: $204$

Answer

The total duration of the diagnostic scan is

204

minutes.

To convert decimal hours to minutes, multiply the total number of hours by

60

. Multiplying

3.4

by

60

equals exactly

204

minutes. Alternatively, this can be calculated by breaking the time into whole and fractional parts:

3

whole hours (

3 \times 60 = 180

minutes) plus

0.4

of an hour (

0.4 \times 60 = 24

minutes). Adding these parts together yields

180 + 24 = 204

minutes.

Step-by-Step Solution

1

Identify the conversion factor for hours to minutes.

1

hour =

60

minutes.

Time units operate on a base-60 system for minutes and hours, not base-10.

2

Multiply the given time in hours by the conversion factor.

3.4 \times 60 = 204

minutes.

This calculation converts the entire decimal value into total minutes.

Key Concept

To convert a time given in decimal hours to minutes, multiply the entire decimal value by

60

. The decimal portion of an hour represents a fraction of

60

minutes, not a direct number of minutes.

Estimated Time:1m 0s

Question 14Question →

A military quartermaster is evaluating the transit times of four different supply routes to an outpost. Arrange the transit times from shortest to longest.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from shortest to longest is: Route Y, Route W, Route X, Route Z.

By converting all durations into minutes, we can compare them accurately. Route Y takes 82 minutes, Route W takes 84 minutes, Route X takes 85 minutes, and Route Z takes 90 minutes. Placing these values in ascending mathematical order gives the correct sequence.

Step-by-Step Solution

1

Identify a common unit for comparison.

Minutes is chosen as the standard unit for all conversions.

Converting all times to a single unit prevents errors when comparing mixed formats.

2

Convert the duration of Route Y to minutes.

1

hour +

22

minutes =

60 + 22 = 82

minutes.

There are

60

minutes in an hour, so we add

60

to the remaining

22

minutes.

3

Convert the duration of Route W to minutes.

1.4 \times 60 = 84

minutes.

Decimal hours are converted to minutes by multiplying the decimal value by

60

.

4

Convert the duration of Route X to minutes.

5,100 \div 60 = 85

minutes.

Because there are

60

seconds in a minute, we divide the total seconds by

60

.

5

Convert the duration of Route Z to minutes.

1.5 \times 60 = 90

minutes.

Fractional hours (

1\frac{1}{2}

hours is

1.5

hours) are multiplied by

60

.

6

Arrange the converted times in ascending order.

82

minutes (Route Y),

84

minutes (Route W),

85

minutes (Route X),

90

minutes (Route Z).

The question specifically asks for the transit times from shortest to longest.

Key Concept

Converting various time formats (decimal hours, fractional hours, seconds, and mixed units) into a standard unit for objective numerical comparison.

Question 15Question →

A chemical processing plant uses a rectangular holding tank measuring $4$ feet long, $3$ feet wide, and $2$ feet deep. The tank is currently filled to exactly $25\%$ of its total capacity with an industrial solvent. The plant manager needs to transfer all of this solvent into small safety bottles that each hold $15$ fluid ounces. Given that $1$ cubic foot holds exactly $7.5$ gallons, and $1$ gallon contains $128$ fluid ounces, what is the maximum number of completely full safety bottles that can be filled from the tank?

144

192

384

1536

Show answer & explanation

Answer: 384

Answer

384

The correct answer is found by first calculating the actual volume of solvent in the tank (

6

cubic feet), converting this volume sequentially through gallons into fluid ounces (

5760

fluid ounces), and finally dividing by the per-bottle capacity (

15

fluid ounces).

Step-by-Step Solution

1

Calculate the total capacity of the rectangular tank.

24

cubic feet

The volume of a rectangular prism is found by multiplying length

\times

width

\times

depth (

4 \times 3 \times 2

).

2

Determine the actual volume of the solvent currently in the tank.

6

cubic feet

The tank is only

25\%

full, so we calculate

0.25 \times 24

.

3

Convert the solvent volume from cubic feet to gallons.

45

gallons

Using the provided conversion factor, multiply the cubic feet by the gallons per cubic foot (

6 \times 7.5

).

4

Convert the solvent volume from gallons to fluid ounces.

5760

fluid ounces

Using the standard conversion factor, multiply the gallons by the fluid ounces per gallon (

45 \times 128

).

5

Calculate the number of completely full bottles.

384

bottles

Divide the total available fluid ounces by the capacity of a single bottle (

5760 \div 15

).

Key Concept

Multi-step volume and capacity conversions incorporating dimensional calculations and partial quantities.

Question 16Question →

A carpenter is preparing to install baseboards in a room. One specific section of the wall requires a continuous board that is exactly $2$ yards and $2$ feet long. What is the required length of this board in inches?

Show answer & explanation

Answer: 96

Answer

The required length of the board is 96 inches.

The correct total length is found by converting all measurements to the same unit. First, 2 yards is converted to 6 feet (

2 \times 3 = 6

). Adding the extra 2 feet gives a total of 8 feet. Finally, converting 8 feet to inches yields 96 inches (

8 \times 12 = 96

). Alternatively, you can convert both to inches directly: 2 yards = 72 inches, and 2 feet = 24 inches. Adding them together gives

72 + 24 = 96

inches.

Step-by-Step Solution

1

Convert the yards measurement to feet.

2 yards = 6 feet.

It is easier to add measurements of the same unit (feet) before finding the final total in inches.

2

Calculate the total length in feet.

6 feet + 2 feet = 8 feet.

This combines both parts of the given measurement into a single unit.

3

Convert the total feet into inches.

8 feet * 12 inches/foot = 96 inches.

The question specifically asks for the final answer in inches, and there are 12 inches in every foot.

Key Concept

Converting compound US Customary linear measurements (yards and feet) into a single smaller unit (inches).

Question 17Question →

A surveyor is mapping four sections of a property perimeter, with measurements recorded in different US customary unit formats. Arrange these four sections in order from the shortest length to the longest length.

Drag items to arrange them in the correct order

Show answer & explanation

Answer

The correct order from shortest to longest is Section P (648 ft), Section Q (659 ft), Section R (660 ft), and Section S (661.5 ft).

To accurately compare these mixed measurements, each value must be mathematically converted to a single common unit, such as feet. Converting yields: Section P = 648 feet, Section Q = 659 feet, Section R = 660 feet, and Section S = 661.5 feet. Sorting these calculated totals produces the correct ascending sequence: Section P, Section Q, Section R, Section S.

Step-by-Step Solution

1

Convert the length of Section P to a standard unit (feet).

528

feet +

120

feet =

648

feet.

\frac{1}{10}

mile

\times 5,280

ft/mile =

528

ft.

40

yards

\times 3

ft/yard =

120

ft.

2

Convert the length of Section Q to feet.

657

feet +

2

feet =

659

feet.

219

yards

\times 3

ft/yard =

657

ft.

24

inches

\div 12

inches/ft =

2

ft.

3

Convert the length of Section R to feet.

660

feet.

\frac{1}{8}

mile

\times 5,280

ft/mile =

660

ft.

4

Convert the length of Section S to feet.

661.5

feet.

7,938

inches

\div 12

inches/ft =

661.5

ft.

5

Order the standardized lengths from shortest to longest.

648

(P) <

659

(Q) <

660

(R) <

661.5

(S).

Comparing all converted values in feet determines the correct physical sequence of lengths.

Key Concept

Converting and comparing mixed US Customary linear measurements (miles, yards, feet, and inches).

Question 18Question →

A cybersecurity team is scheduled to run a continuous diagnostic scan on a network grid. The scan requires exactly $5.4$ hours to complete. If the team initiates the scan at $22:45$ , at what time will the scan finish?

04:09

04:25

03:51

03:49

Show answer & explanation

Answer: $04:09$

Answer

The scan will finish at

04:09

.

To find the finish time, the total duration of

5.4

hours must first be converted into hours and minutes. The

0.4

hours is equal to

0.4 \times 60 = 24

minutes, making the total duration

5

hours and

24

minutes. Starting at

22:45

, adding

5

hours crosses midnight (

24:00

) and lands at

03:45

the next day. Adding the remaining

24

minutes to

03:45

yields the final time of

04:09

.

Step-by-Step Solution

1

Convert the decimal portion of the scan duration into minutes.

0.4 \text{ hours} \times 60 \text{ minutes/hour} = 24 \text{ minutes}

. The total duration is

5

hours and

24

minutes.

Time is measured in base-60, so fractional hours must be multiplied by 60 to find the equivalent minutes.

2

Add the whole hours to the starting time.

22:45 + 5 \text{ hours} = 27:45

. Subtracting

24

hours for the crossover into the next day gives

03:45

.

This establishes the hour portion of the finish time on the following day.

3

Add the remaining minutes to the adjusted time.

03:45 + 24 \text{ minutes} = 04:09

.

Adding the

24

minutes yields the final completion time.

Key Concept

Converting decimal hours to minutes (base-60) and calculating elapsed time across the midnight boundary.

Question 19Question →

A tailor is combining two pieces of fabric to make a continuous banner. One piece is $3 \frac{1}{2}$ yards long, and the second piece is $1 \frac{1}{4}$ yards long. After joining them together end-to-end, the tailor needs to cut the combined fabric into smaller segments that are each $15$ inches long. How many complete segments can the tailor cut from the combined fabric?

11

10

9

3

Show answer & explanation

Answer: 11

Answer

11

The total length of the fabric is found by adding

3 \frac{1}{2}

yards and

1 \frac{1}{4}

yards, which equals

4 \frac{3}{4}

yards. Because there are

36

inches in one yard, this is equivalent to

4.75 \times 36 = 171

inches. Dividing the total

171

inches by the required segment length of

15

inches gives

11.4

. Therefore,

11

complete segments can be cut.

Step-by-Step Solution

1

Calculate the total length of the fabric in yards.

3 \frac{1}{2} + 1 \frac{1}{4} = 3 \frac{2}{4} + 1 \frac{1}{4} = 4 \frac{3}{4} \text{ yards}

The two pieces are joined end-to-end, requiring addition with a common denominator.

2

Convert the total length from yards to inches.

4 \frac{3}{4} \text{ yards} \times 36 \text{ inches/yard} = 171 \text{ inches}

The target segment length is in inches, so the total fabric length must share the same unit before dividing.

3

Divide the total inches by the length of one segment.

171 \div 15 = 11.4

Division determines how many

15

-inch segments fit into the

171

-inch length.

4

Identify the number of complete segments.

11

The tailor can only use whole, complete segments, so the decimal remainder is dropped.

Key Concept

Multi-step conversion of US customary linear units involving mixed fractions.

Estimated Time:1m 15s

Question 20Question →

A supply depot receives a shipment of $1.8$ tons of emergency rations. The personnel first distribute the rations into 24 bulk storage containers, placing exactly 50 pounds into each container. The remaining rations are then divided into individual meal packets that contain 15 ounces each. How many complete 15-ounce meal packets can be filled from the remaining rations?

10

160

1600

2560

Show answer & explanation

Answer: 2560

Answer

2560

The correct answer is found by first converting the 1.8 tons to 3,600 pounds. Next, subtract the 1,200 pounds used for the bulk containers to get 2,400 pounds remaining. Convert this remainder to ounces by multiplying by 16, yielding 38,400 ounces. Finally, dividing by the 15-ounce packet size results in exactly 2,560 packets.

Step-by-Step Solution

1

Convert the total weight of the shipment from tons to pounds.

1.8 \times 2000 = 3600

pounds

Standardizing the initial weight into pounds is required because the bulk containers are measured in pounds.

2

Calculate the total weight placed into the bulk storage containers.

24 \times 50 = 1200

pounds

This establishes how much of the shipment has already been allocated.

3

Subtract the bulk storage weight from the total weight to find the remaining pounds.

3600 - 1200 = 2400

pounds

This isolates the remaining weight that will be used for the individual meal packets.

4

Convert the remaining weight from pounds to ounces.

2400 \times 16 = 38400

ounces

The meal packets are measured in ounces, so the remaining bulk weight must match these units before dividing.

5

Divide the remaining ounces by the size of each meal packet.

38400 \div 15 = 2560

packets

This final division determines the exact number of packets that can be completely filled.

Key Concept

Multi-step conversion between US Customary weight units (tons, pounds, ounces)

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