A reservoir initially contains 4,800 gallons of water. A drainage pump operates at a const… — GRE General Test

A reservoir initially contains $4,800$ gallons of water. A drainage pump operates at a constant rate of $120$ gallons per minute to empty the reservoir. How many minutes of continuous pumping will it take for the amount of water remaining in the reservoir to be reduced to $1,200$ gallons?

A
$10$
B
$25$
$30$ Answer
D
$40$
E
$50$

Answer

30 minutes

To find the time needed for

1,200

gallons to remain, subtract

1,200

from the initial

4,800

gallons to determine that

3,600

gallons of water must be removed. Dividing the

3,600

gallons by the drainage rate of

120

gallons per minute gives exactly

30

minutes.

Step-by-Step Solution

Calculate the total volume of water that must be drained from the reservoir.

4,800 \text{ gallons} - 1,200 \text{ gallons} = 3,600 \text{ gallons}

The question asks for the time until

1,200

gallons remain, so the amount removed is the difference between the starting volume and ending volume.

Set up the linear rate equation to solve for elapsed time

t

in minutes.

\text{Rate} \times t = \text{Volume Drained} \implies 120t = 3,600

The rate of drainage is constant at

120

gallons per minute.

Solve for

t

t = \frac{3,600}{120} = 30 \text{ minutes}

Dividing total gallons to drain by the rate gives the required time.

Key Concept

Linear Modeling and Distance-Rate-Time / Work-Rate Relationships

Estimated Time:1m 0s

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