A military water purification unit has three filters operating at different unit rates. Fi… — Armed Services Vocational Aptitude Battery (ASVAB)

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

Answer: 210 minutes

Answer

210

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

Step-by-Step Solution

Calculate the unit rate for Filter X.

120

gallons per hour

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

180 \div 1.5 = 120

Calculate the unit rate for Filter Y.

160

gallons per hour

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

320 \div 2 = 160

Calculate the unit rate for Filter Z.

144

gallons per hour

Filter Z operates

20\%

faster than Filter X, so its rate is

120 + (0.20 \times 120) = 144

Calculate the combined unit rate of all three filters.

424

gallons per hour

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

120 + 160 + 144 = 424

Determine the time in hours needed to purify

1,484

gallons.

3.5

hours

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

1,484 \div 424 = 3.5

Convert the total time from hours to minutes.

210

minutes

The question explicitly asks for the answer in minutes.

3.5 \times 60 = 210

Key Concept

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

Alternative Method

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

Estimated Time:3m 30s

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