Direct Proportions Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

A commercial 3D printer extrudes $1.2$ kilograms of plastic filament every $45$ minutes of operation. Assuming the printer continues to operate at this exact constant rate, how many grams of filament will it extrude during a $3$ -hour continuous printing session?

4.8

80

300

4800

Show answer & explanation

Answer: $4800$

Answer

The printer will extrude 4800 grams of filament.

Solving this requires maintaining consistent units while scaling up the operation time. Converting the 3-hour print session into 180 minutes reveals that the printer operates for exactly 4 times the duration of the baseline 45-minute period (180 divided by 45 is 4). Because the relationship is a direct proportion, the mass of filament used also scales by a factor of 4. Multiplying 1.2 kilograms by 4 yields 4.8 kilograms. Finally, converting 4.8 kilograms into grams by multiplying by 1000 gives 4800 grams.

Step-by-Step Solution

1

Convert the target time period from hours to minutes to match the units of the given rate.

3 \text{ hours} = 3 \times 60 = 180 \text{ minutes}

Units must be consistent across the proportion equation to find the correct multiplier.

2

Set up a direct proportion to find the amount of filament extruded in kilograms over the new time period.

\frac{1.2 \text{ kg}}{45 \text{ min}} = \frac{x \text{ kg}}{180 \text{ min}} \Rightarrow x = 1.2 \times \left(\frac{180}{45}\right) = 1.2 \times 4 = 4.8 \text{ kg}

The mass of filament extruded scales directly with the time the machine operates.

3

Convert the resulting mass from kilograms to grams.

4.8 \text{ kg} = 4.8 \times 1000 = 4800 \text{ grams}

The question specifically asks for the final answer in grams.

Key Concept

Direct Proportions with Unit Conversions

Question 2Question →

Determine the correct numerical values to complete the statement.

Fill in the blanks below

An aviation mechanic calibrates

8

flight instruments in

3

hours. If a squadron requires

20

instruments to be calibrated, and the mechanic works at the same constant rate, it will take hours and minutes to complete the task.

Show answer & explanation

Answer

It will take 7 hours and 30 minutes.

Because the work rate is constant, the number of instruments calibrated is directly proportional to the time taken. Setting up the proportion 8/3 = 20/x yields x = 7.5 hours. Converting the remaining 0.5 hours to minutes gives 30 minutes, resulting in a total required time of 7 hours and 30 minutes.

Step-by-Step Solution

1

Set up a direct proportion comparing the number of instruments to the time in hours.

\frac{8 \text{ instruments}}{3 \text{ hours}} = \frac{20 \text{ instruments}}{x \text{ hours}}

When a rate is constant, the ratio of work completed to time taken remains equivalent.

2

Cross-multiply the terms to create a linear equation.

8x = 3 \times 20

Cross-multiplying is the standard algebraic method to solve for an unknown in a proportional relationship.

3

Simplify the equation and solve for

x

.

8x = 60 \Rightarrow x = \frac{60}{8} = 7.5 \text{ hours}

Isolating

x

provides the total required time expressed in hours.

4

Convert the decimal portion of the hours into minutes.

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

The question specifically requires the final answer to be formatted in hours and minutes.

Key Concept

Direct proportions with unit conversion

Estimated Time:1m 30s

Question 3Question →

A high-capacity water pump transfers $840$ gallons of water in $15$ minutes. Operating at this exact constant rate, how many gallons of water will the pump transfer in $3.5$ hours?

60

196

1,176

11,760

Show answer & explanation

Answer: $11,760$

Answer

The pump will transfer 11,760 gallons of water in 3.5 hours.

The problem describes a direct proportion between water volume and time. First, the unit rate is found by dividing

840

gallons by

15

minutes, which gives

56

gallons per minute. Then, the target time of

3.5

hours is converted to

210

minutes (

3.5 \times 60

). Multiplying the unit rate of

56

gallons per minute by the

210

minutes yields

11,760

gallons.

Step-by-Step Solution

1

Find the unit rate of the pump in gallons per minute.

840 \div 15 = 56

gallons per minute.

To establish a common base rate that can be scaled to any duration.

2

Convert the target time from hours to minutes.

3.5 \times 60 = 210

minutes.

Proportions require consistent units across all terms; the rate is in minutes, so the target time must also be in minutes.

3

Multiply the unit rate by the total number of minutes.

56 \times 210 = 11,760

gallons.

To find the total volume transferred at the constant rate over the specified time period.

Key Concept

Direct Proportions

Alternative Method

Instead of finding the unit rate per minute, you can find the rate per hour. Since 15 minutes is

1/4

of an hour, multiply 840 by 4 to get

3,360

gallons per hour. Then, multiply

3,360

by

3.5

hours to get

11,760

gallons.

Estimated Time:1m 0s

Question 4Question →

Fill in the blank with the correct numeric value to complete the statement.

Fill in the blanks below

A printing press can print

50

identical banners in

2

minutes. At this constant rate, the press will print banners in

10

minutes.

Show answer & explanation

Answer

250

Because the printing press operates at a constant rate, the number of banners produced is directly proportional to the time spent printing. Since

10

minutes is exactly

5

times longer than the initial

2

minutes, the press will produce

5

times as many banners. Multiplying the original

50

banners by

5

results in

250

banners.

Step-by-Step Solution

1

Identify the given ratio of banners to time.

The press produces

50

banners per

2

minutes.

Establishing the baseline rate is the first step in setting up a direct proportion.

2

Determine the scaling factor for the time.

The time increases from

2

minutes to

10

minutes. The scaling factor is

\frac{10}{2} = 5

.

Finding how many times greater the new time is compared to the original time tells us how to scale the output.

3

Multiply the baseline production by the scaling factor.

50 \times 5 = 250

banners.

In a direct proportion, as time increases by a certain multiple, the quantity produced increases by that exact same multiple.

Key Concept

Direct Proportions

Question 5Question →

A supply pump transfers $10$ gallons of aviation fuel every $15$ seconds. At this rate, how many gallons of fuel will it transfer in $3$ minutes?

120

270

12

2

Show answer & explanation

Answer: 120

Answer

120

The problem establishes a constant rate, which requires a direct proportion to solve. First, convert the

3

-minute time period into

180

seconds to match the units of the given rate. Then, set up the proportion

\frac{10}{15} = \frac{x}{180}

. Cross-multiplying

10

by

180

yields

1800

, and dividing that product by

15

results in

120

gallons.

Step-by-Step Solution

1

Harmonize the time units by converting minutes to seconds.

3

minutes

= 3 \times 60 = 180

seconds.

The initial rate is given in seconds, so the target time must also be in seconds to set up an accurate mathematical proportion.

2

Set up a direct proportion using the given rate.

10

gallons /

15

seconds

= x

gallons /

180

seconds.

The pump operates at a constant rate, meaning the ratio of volume to time remains equivalent.

3

Solve for the unknown volume

x

.

x = \frac{10 \times 180}{15} = \frac{1800}{15} = 120

gallons.

Cross-multiplying and dividing isolates the variable, providing the total gallons transferred.

Key Concept

Direct proportions represent situations where two quantities increase at the same relative rate. When setting up proportions, it is critical to ensure that corresponding units match.

Question 6Question →

An industrial cleaning solvent requires a mixture of Chemical A and Chemical B in a ratio of $5:2$ by volume. If a worker uses $300$ milliliters of Chemical B, how many liters of the final cleaning solvent will be produced?

1050

0.75

1.05

10.5

Show answer & explanation

Answer: 1.05

Answer

1.05

The correct answer accurately scales the mixture from parts to a total volume. Since the ratio of Chemical A to B is 5:2, there are 7 total parts in the mixture. Chemical B makes up 2 of these 7 parts. Setting up the proportion 2/7 = 300/x gives a total volume of 1050 mL. Converting this volume to liters by dividing by 1000 results in 1.05 liters.

Step-by-Step Solution

1

Identify the ratio of Chemical B to the total mixture.

The mixture has 5 parts Chemical A and 2 parts Chemical B, making 7 total parts. The ratio of Chemical B to the total is 2:7.

To find the total volume based on the volume of one component, we need the part-to-whole relationship.

2

Set up and solve a proportion to find the total volume in milliliters.

2 / 7 = 300 / x. Cross-multiplying gives 2x = 2100, which simplifies to x = 1050 milliliters.

Direct proportions allow us to scale the ratio up to find the actual combined volume of the mixture.

3

Convert the total volume from milliliters to liters.

1050 / 1000 = 1.05 liters.

The question explicitly requires the final answer to be stated in liters.

Key Concept

Direct proportions and unit conversions in part-to-whole relationships

Alternative Method

Instead of setting up a formal proportion, use the unitary method. If 2 parts represent 300 mL, then 1 part equals 150 mL (300 / 2). The total mixture requires 7 parts, so the total volume is 7 * 150 = 1050 mL. Converting to liters gives 1.05 L.

Estimated Time:1m 30s

Question 7Question →

Solve the following word problem by calculating the missing value.

Fill in the blanks below

An engineering battalion can lay

40

feet of runway matting in

15

minutes. Operating at this constant rate, the battalion will lay feet of matting in

1.5

hours.

Show answer & explanation

Answer

240

Because

1.5

hours is equivalent to

90

minutes, the time period is exactly

6

times longer than the original

15

-minute period (

90 \div 15 = 6

). In a direct proportion, the amount of matting laid increases by the same factor, so

40 \text{ feet} \times 6 = 240 \text{ feet}

.

Step-by-Step Solution

1

Convert the target time frame into the same units used for the known rate.

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

Units of time must match to set up a valid direct proportion.

2

Set up a proportion relating feet of matting to minutes.

\frac{40 \text{ feet}}{15 \text{ minutes}} = \frac{x \text{ feet}}{90 \text{ minutes}}

Because the rate is constant, the ratio of distance to time remains the same.

3

Solve for the unknown value

x

.

x = \frac{40 \times 90}{15} = 40 \times 6 = 240

Isolating

x

provides the total feet of matting laid in

90

minutes.

Key Concept

Direct proportions with unit conversion

Question 8Question →

A maintenance crew can paint $120$ square feet of a ship's hull in $2$ hours. Working at this same constant rate, how many square feet can the crew paint in $5$ hours?

Show answer & explanation

Answer: 300

Answer

300

Because the work happens at a constant rate, the area painted is directly proportional to the time spent working. Finding the unit rate (

60

square feet per hour) and multiplying it by the target time (

5

hours) yields the correct total of

300

square feet.

Step-by-Step Solution

1

Calculate the unit rate of painting.

60

square feet per hour

To find how much is painted in a different amount of time, we first need to know how much is painted in one hour. We do this by dividing the total area (

120

) by the total time (

2

).

2

Calculate the total area painted in the new timeframe.

300

square feet

Multiply the unit rate (

60

square feet per hour) by the new target time (

5

hours) to find the final proportional amount.

Key Concept

Direct Proportions

Question 9Question →

A commercial bakery makes a standard pastry dough using a ratio of $7$ parts flour to $3$ parts butter by weight. If a daily batch requires $42$ pounds of flour, how many pounds of butter are needed?

18

60

98

126

Show answer & explanation

Answer: $18$

Answer

18

The ratio of flour to butter is given as

7:3

. Setting up a direct proportion where

x

is the pounds of butter needed:

\frac{7}{3} = \frac{42}{x}

. Cross-multiplying gives

7x = 126

. Solving for

x

yields

x = 18

pounds of butter.

Step-by-Step Solution

1

Identify the given ratio and the known quantity.

The ratio of flour to butter is

7:3

. The known quantity of flour is

42

pounds.

To set up a proportion, we must align the correct parts of the ratio with the real-world amounts.

2

Set up a direct proportion equation.

\frac{7}{3} = \frac{42}{x}

The ratio of parts must equal the ratio of the actual weights.

3

Solve for the unknown value

x

.

7x = 3 \times 42 \rightarrow 7x = 126 \rightarrow x = 18

Cross-multiplying and dividing isolates the variable to find the required pounds of butter.

Key Concept

Direct Proportions

Question 10Question →

An automated wire-cutting machine processes $350$ meters of copper wiring in $20$ minutes. Operating at this constant rate, how many meters of wiring will the machine process in $1.5$ hours?

Show answer & explanation

Answer: 1575

Answer

1575

Because the machine operates at a constant rate, the relationship between time and wire processed is directly proportional. However, the time units differ between the given rate (

20

minutes) and the target time (

1.5

hours). First, convert

1.5

hours to

90

minutes. Then, set up the direct proportion

\frac{350 \text{ meters}}{20 \text{ minutes}} = \frac{x \text{ meters}}{90 \text{ minutes}}

. Solving for

x

by multiplying

350

by

90

and dividing by

20

yields exactly

1575

meters.

Step-by-Step Solution

1

Harmonize the time units by converting hours to minutes.

90

minutes

The given rate is in meters per minute, so the target time must also be in minutes to establish a valid equivalent ratio.

2

Set up a direct proportion equation.

\frac{350}{20} = \frac{x}{90}

The length of wire processed increases at a constant, directly proportional rate to the time operated.

3

Solve the proportion for the unknown value

x

.

x = 1575

Cross-multiplying and simplifying isolates

x

, calculating the total meters processed in the longer timeframe.

Key Concept

Direct proportions with unit harmonization

Question 11Question →

A field water purification system processes $12.5$ gallons of clean water every $5$ minutes. Operating at this same constant rate, how many gallons of clean water will the system process in $2$ hours?

5

30

48

300

Show answer & explanation

Answer: 300

Answer

The system will process 300 gallons of clean water in 2 hours.

The correct answer accurately harmonizes the time units by converting 2 hours into 120 minutes, and then scales the given volume-to-time ratio (

12.5

gallons per

5

minutes) up to

120

minutes, resulting in

300

gallons.

Step-by-Step Solution

1

Convert the target time into the same units used in the given rate.

2

hours

= 2 \times 60 = 120

minutes.

Proportions require matching units to accurately compare the two ratios.

2

Calculate the unit rate of water processed per minute.

12.5 \text{ gallons} \div 5 \text{ minutes} = 2.5 \text{ gallons per minute}

.

Finding the amount processed in one minute simplifies scaling up to the total time.

3

Multiply the unit rate by the total number of minutes.

2.5 \text{ gallons/minute} \times 120 \text{ minutes} = 300 \text{ gallons}

.

This applies the constant rate over the entire duration to find the total volume.

Key Concept

Direct proportions with unit conversion

Question 12Question →

A specialized construction $3$ D printer uses $2.4$ metric tons of concrete to print $15$ linear feet of a wall. At this constant rate, how many kilograms of concrete are required to print a wall that is $25$ yards long? ( $1$ metric ton = $1,000$ kilograms; $1$ yard = $3$ feet)

4,000

1,200

12,000

480

Show answer & explanation

Answer: $12,000$

Answer

The correct answer is

12,000

.

The correct answer is found by harmonizing the length units, determining the scaled proportion, and harmonizing the final weight units. Converting

25

yards to

75

feet reveals that the target length is

5

times the initial length (

75 \div 15 = 5

). Multiplying the initial concrete requirement by this scale factor yields

12

metric tons (

2.4 \times 5 = 12

). Finally, converting

12

metric tons to kilograms yields

12,000

kilograms.

Step-by-Step Solution

1

Convert the target length from yards to feet.

25 \text{ yards} = 25 \times 3 = 75 \text{ feet}

.

The units of length must match the given rate (

15

linear feet) before setting up a proportion.

2

Set up a direct proportion to find the metric tons of concrete needed.

\frac{2.4}{15} = \frac{x}{75}

The amount of concrete used is directly proportional to the length of the wall printed.

3

Solve the proportion for

x

.

x = \frac{2.4 \times 75}{15} = 2.4 \times 5 = 12 \text{ metric tons}

.

Isolating

x

provides the required amount of concrete in metric tons.

4

Convert metric tons to kilograms.

12 \text{ metric tons} = 12 \times 1,000 = 12,000 \text{ kilograms}

.

The question specifically asks for the final answer in kilograms.

Key Concept

Direct Proportions with Unit Conversions

Question 13Question →

An earth-moving excavator clears $120$ cubic yards of debris in $45$ minutes. Operating at this constant rate, how many cubic yards of debris will the excavator clear in $3$ hours?

480

8

30

48

Show answer & explanation

Answer: 480

Answer

480

The correct answer is found by first converting

3

hours into

180

minutes. Then, applying a direct proportion,

\frac{120}{45} = \frac{x}{180}

, yields

x = 480

. Alternatively, observing that

180

minutes is exactly

4

times as long as

45

minutes means the excavator will clear

4

times the debris:

120 \times 4 = 480

.

Step-by-Step Solution

1

Convert the target time from hours to minutes so the units match the given rate.

3 \text{ hours} \times 60 \text{ minutes/hour} = 180 \text{ minutes}

Units of time must be identical before setting up a valid proportion.

2

Set up a direct proportion relating the volume of debris to the time taken.

\frac{120}{45} = \frac{x}{180}

Since the excavator works at a constant rate, the ratio of volume to time remains constant.

3

Solve for the unknown volume (

x

) by cross-multiplying or finding a common multiplier.

x = \frac{120 \times 180}{45} = 120 \times 4 = 480

Isolating

x

provides the total cubic yards cleared in

180

minutes.

Key Concept

Direct proportions with unit conversions

Estimated Time:1m 0s

Question 14Question →

Determine the correct numerical value to complete the statement below based on the provided rates.

Fill in the blanks below

An airborne logistics division drops

3.5

tons of humanitarian rations every

12

minutes. Operating at this constant rate, the division will drop pounds of rations in

1.5

hours.

*(Note:

1 \text{ ton} = 2,000 \text{ pounds}

)*

Show answer & explanation

Answer

52,500

The scenario requires calculating a proportional amount while successfully navigating two unit conversions. First, harmonize the time units by converting

1.5

hours to

90

minutes. Next, convert the initial weight of

3.5

tons into

7,000

pounds. Using these standardized units, set up the proportion:

7,000 \text{ lbs} / 12 \text{ min} = x \text{ lbs} / 90 \text{ min}

. Cross-multiplying gives

12x = 630,000

, and dividing by

12

results in exactly

52,500

pounds.

Step-by-Step Solution

1

Convert the target time frame from hours to minutes so it matches the time unit in the given rate.

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

Direct proportions require time units to be identical across both ratios.

2

Convert the initial weight from tons to pounds to match the requested unit for the final answer.

3.5 \text{ tons} \times 2,000 \text{ pounds/ton} = 7,000 \text{ pounds}

Harmonizing the weight units prevents conversion errors at the end of the calculation.

3

Set up a direct proportion equation comparing weight to time.

\frac{7,000 \text{ pounds}}{12 \text{ minutes}} = \frac{x \text{ pounds}}{90 \text{ minutes}}

Because the drop rate is constant, the ratio of weight to time remains equal.

4

Solve for the unknown weight (x).

x = \frac{7,000 \times 90}{12} = \frac{630,000}{12} = 52,500 \text{ pounds}

Cross-multiplying and dividing isolates the variable, yielding the total pounds dropped over the full time period.

Key Concept

Setting up and solving a direct proportion after performing multiple unit conversions.

Question 15Question →

Read the scenario and fill in the blank with the correct numerical value.

Fill in the blanks below

A logistics team can pack

30

ration boxes in

15

minutes. Operating at this same constant rate, the team can pack ration boxes in

45

minutes.

Show answer & explanation

Answer

90

Because the packing rate is constant, the relationship between boxes and minutes is directly proportional. Determining the unit rate (

2

boxes per minute) and multiplying it by the target time (

45

minutes) correctly yields

90

boxes.

Step-by-Step Solution

1

Calculate the unit rate of packing.

30 \div 15 = 2

boxes per minute.

To find out how many boxes can be packed in a different amount of time, it helps to first know how many boxes are packed in exactly one minute.

2

Multiply the unit rate by the new time.

2 \times 45 = 90

boxes.

Since the team packs 2 boxes every minute, multiplying this constant rate by 45 minutes gives the total number of boxes packed in that timeframe.

Key Concept

Direct Proportions

Alternative Method

You can also solve this by setting up a direct proportion equation:

\frac{30}{15} = \frac{x}{45}

. Recognizing that

45

is exactly

3

times

15

, you can simply multiply the initial number of boxes by

3

:

30 \times 3 = 90

.

Estimated Time:45s

Question 16Question →

An industrial textile loom weaves $4.5$ yards of heavy canvas every $12$ minutes. Operating at this same constant rate, how many feet of canvas will the loom produce during a complete $8$ -hour work shift?

Show answer & explanation

Answer: 540

Answer

540 feet

To solve this problem, you must properly scale a direct proportion while paying careful attention to units. First, harmonize the time units: an 8-hour shift is equal to 480 minutes (8 × 60). Next, set up a proportion or find the scale factor: 480 minutes is exactly 40 times longer than the 12-minute baseline (480 ÷ 12 = 40). Because the loom operates at a constant rate, it will produce 40 times as much canvas. Multiply the 4.5 yards by 40 to find the total yards produced (4.5 × 40 = 180 yards). Finally, the question asks for the answer in feet. Since there are 3 feet in 1 yard, multiply 180 yards by 3 to get exactly 540 feet.

Step-by-Step Solution

1

Convert the total operating time from hours to minutes to match the given rate's unit of time.

8 \text{ hours} \times 60 \text{ minutes/hour} = 480 \text{ minutes}

Units of time must be identical before calculating the direct proportion.

2

Determine how many 12-minute intervals occur in the 480-minute shift.

480 \div 12 = 40 \text{ intervals}

This establishes the multiplier (scale factor) that will be applied to the fabric production.

3

Calculate the total yards of canvas produced during the entire shift.

40 \times 4.5 \text{ yards} = 180 \text{ yards}

Because production is directly proportional to time, multiplying the base production by the time scale factor yields total yards.

4

Convert the total production from yards to feet to answer the specific question asked.

180 \text{ yards} \times 3 \text{ feet/yard} = 540 \text{ feet}

The stem explicitly asks for the final length in feet, making this unit conversion a critical final step.

Key Concept

Solving multi-step direct proportion problems that require initial and final unit harmonizations (time and length).

Question 17Question →

A portable generator consumes $8$ liters of fuel every $12$ hours of operation. At this constant rate, how many liters of fuel will the generator consume in $48$ hours of operation?

2

3.2

32

72

Show answer & explanation

Answer: 32

Answer

The generator will consume 32 liters of fuel.

Because the generator operates at a constant rate, the relationship between time and fuel is a direct proportion. The new operating time (

48

hours) is exactly

4

times longer than the original operating time (

12

hours). Therefore, the fuel consumption will also be

4

times greater:

8 \text{ liters} \times 4 = 32 \text{ liters}

.

Step-by-Step Solution

1

Determine the relationship between the two operating times.

48 \div 12 = 4

Finding the scale factor makes it simple to calculate the proportionally larger amount of fuel.

2

Multiply the original fuel amount by the scale factor.

8 \times 4 = 32

liters

In a direct proportion, whatever factor scales the time must also scale the fuel consumption.

Key Concept

Direct proportions state that as one quantity increases by a certain multiplier, the related quantity increases by that exact same multiplier.

Question 18Question →

Complete the statement below by calculating the missing numerical value. Enter only the number.

Fill in the blanks below

A military satellite uplink transmits

1.5

gigabytes of reconnaissance data every

40

seconds. Operating at this constant rate, it will take minutes to transmit a total of

18

gigabytes of data.

Show answer & explanation

Answer

8

By setting up a proportion, we find that transmitting

18

gigabytes takes

480

seconds. Dividing

480

seconds by

60

gives exactly

8

minutes.

Step-by-Step Solution

1

Set up a direct proportion comparing data volume to time.

\frac{1.5}{40} = \frac{18}{x}

Because the transmission rate is constant, the ratio of gigabytes to seconds remains the same.

2

Solve for the unknown time

x

in seconds by cross-multiplying.

1.5x = 40 \times 18 \rightarrow 1.5x = 720 \rightarrow x = 480

seconds

Cross-multiplication isolates the variable, giving the total time required in seconds.

3

Convert the total seconds into minutes.

480 \div 60 = 8

minutes

The question specifically asks for the time in minutes, so the time in seconds must be divided by the number of seconds in a minute (

60

).

Key Concept

Direct proportions with unit conversions

Estimated Time:1m 30s

Question 19Question →

A naval vessel's desalination plant produces fresh water at a rate directly proportional to its operational time. The plant produces $1,500$ liters of fresh water in $40$ minutes. The vessel's main storage tank has a total capacity of $24$ cubic meters and is currently $25\%$ full.

Assuming $1$ cubic meter equals $1,000$ liters, determine the correct numerical value to answer the question: How many continuous hours must the desalination plant operate to completely fill the remainder of the storage tank?

Fill in the blanks below

The plant must operate for hours.

Show answer & explanation

Answer

8

The correct answer is 8 hours. First, convert the tank capacity to liters:

24 \text{ m}^3 = 24,000 \text{ L}

. Since the tank is

25\%

full, it needs

75\%

of its capacity to be filled, which is

24,000 \times 0.75 = 18,000 \text{ L}

. Using the direct proportion

\frac{40}{1,500} = \frac{x}{18,000}

, we find

x = 480

minutes. Finally, converting minutes to hours by dividing by

60

gives exactly

8

hours.

Step-by-Step Solution

1

Calculate the total tank capacity in liters.

24 \times 1,000 = 24,000

liters.

To harmonize the tank's volume units with the desalination plant's production rate, which is given in liters.

2

Determine the volume of water needed to fill the remainder of the tank.

24,000 \times (1 - 0.25) = 18,000

liters.

The tank is already

25\%

full, meaning only the remaining

75\%

needs to be produced.

3

Set up and solve a direct proportion to find the required time in minutes.

\frac{40 \text{ min}}{1,500 \text{ L}} = \frac{x \text{ min}}{18,000 \text{ L}} \Rightarrow x = \frac{40 \times 18,000}{1,500} = 480

minutes.

Because water production is directly proportional to operational time.

4

Convert the required time from minutes to hours.

480 \div 60 = 8

hours.

The question specifically asks for the operational time in continuous hours.

Key Concept

Solving multi-step direct proportions involving unit harmonization and percentages.

Question 20Question →

A naval ship uses $400$ pounds of provisions to feed a specific crew for $5$ days. At this same constant rate, how many pounds of provisions are needed to feed the crew for $12$ days?

Show answer & explanation

Answer: 960

Answer

960

By determining the unit rate of

80

pounds per day and multiplying it by

12

days, the direct proportionality rule is correctly applied to find the total of

960

pounds.

Step-by-Step Solution

1

Calculate the unit rate of provisions per day.

400 \div 5 = 80

pounds per day.

Finding the amount used in one day allows scaling the proportion to any other number of days.

2

Multiply the unit rate by the new number of days.

80 \times 12 = 960

pounds.

This scales the daily rate up to the required

12

-day period to maintain the direct proportion.

Key Concept

Direct proportions using unit rates

Estimated Time:45s

Direct Proportions

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes