A naval vessel's desalination plant produces fresh water at a rate directly proportional t… — Armed Services Vocational Aptitude Battery (ASVAB)

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?

Answer:The plant must operate for 【8】 hours.

Answer

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

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.

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.

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.

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.

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