Question

Water comes out of a garden hose at a constant rate to fill a pool. After 3 minutes, the pool is filled with 30 gallons of water. After 6.5 minutes, the pool is filled with 65 gallons of water.

a. Write an equation that represents the number of gallons of water y in the pool after x minutes.
b. How long will it take to fill a pool that needs 10,000 gallons of water?

Answer 1

a. y = 10x

b. 1000 minutes of 16 2/3 hours

Explanation:

a.

30 gal / 3 min = 10 gal/min

65 gal / 6.5 min = 10 gal/min

The relation is a direct proportion.

y = kx

The filling rate is the slope which is also the constant of proportionality.

The equation is

y = 10x

b.

y = 10x

10,000 = 10x

x = 10,000/10

x = 1000

The time is 1000 minutes, or 16 2/3 hours.