A water desalination plant processes seawater using two filtration units, Unit P and Unit … — ACT

A water desalination plant processes seawater using two filtration units, Unit P and Unit Q. Unit P can process $720$ gallons of water in $45$ minutes. Unit Q processes water at a rate that is $25\%$ faster than Unit P. If both units operate continuously at their respective rates, how many total gallons of water can Unit P and Unit Q process combined in $2.5$ hours?

A
$3,000$
B
$4,200$
$5,400$ Answer
D
$8,550$
E
$9,000$

Answer

5,400

gallons

Unit P processes water at a rate of

16

gallons per minute (

720 \div 45

). Unit Q operates

25\%

faster, making its rate

20

gallons per minute (

16 \times 1.25

). Working simultaneously, their combined rate is

36

gallons per minute (

16 + 20

). Converting

2.5

hours into

150

minutes (

2.5 \times 60

) and multiplying by the combined rate gives a total of

36 \times 150 = 5,400

gallons.

Step-by-Step Solution

Calculate the unit processing rate of Unit P per minute.

\frac{720 \text{ gallons}}{45 \text{ minutes}} = 16 \text{ gallons per minute}

Divide the total gallons processed by Unit P by the number of minutes to find its unit rate.

Determine the unit processing rate of Unit Q per minute.

16 \times (1 + 0.25) = 20 \text{ gallons per minute}

Unit Q is 25% faster than Unit P, so multiply Unit P's rate by 1.25.

Calculate the combined processing rate of both units.

16 + 20 = 36 \text{ gallons per minute}

Add the individual rates of Unit P and Unit Q to get their joint processing speed.

Convert 2.5 hours to minutes and calculate the combined total gallons processed.

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

;

36 \times 150 = 5,400 \text{ gallons}

Multiply the combined rate per minute by the total operating time in minutes.

Key Concept

Unit rate calculation and proportional scaling across multiple rate sources

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