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The water level in a rectangular pool that is 80 ft wide and 160 ft long is changing at a rate of -1/4 inch per day. How many gallons of water is the pool losing? Show your work.

(Note: 1 cubic foot = 7.5 gallons)

Answer :

The pool is losing 2000 gallons of water per day.

To determine how many gallons of water the pool is losing, we need to calculate the volume of water being lost per day and then convert that volume into gallons.


Since the pool is rectangular and has dimensions of 80 ft (width) and 160 ft (length), the surface area (A) is:

[tex]A = 80 \text{ ft} \times 160 \text{ ft} = 12800 \text{ ft}^2[/tex]


The water level is changing at a rate of [tex]-\frac{1}{4}[/tex] inch per day. First, convert this rate to feet:

[tex]-\frac{1}{4} \text{ inch/day} = -\frac{1}{4} \times \frac{1}{12} \text{ ft/inch} = -\frac{1}{48} \text{ ft/day}[/tex]

Now, the volume of water lost per day (V) can be found by multiplying the surface area (A) by the change in water level (height, h):

[tex]V = A \times h = 12800 \text{ ft}^2 \times -\frac{1}{48} \text{ ft} = -266.67 \text{ ft}^3[/tex]

Convert the volume from cubic feet to gallons:
Since 1 cubic foot is equal to 7.5 gallons, the number of gallons lost per day (G) is:

[tex]G = V \times 7.5 \frac{\text{gallons}}{\text{ft}^3} = -266.67 \text{ ft}^3 \times 7.5 \frac{\text{gallons}}{\text{ft}^3} = -2000 \text{ gallons}[/tex]

Negative sign indicates the loss in volume of water.
∴ G = 2000 gallon

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