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Two hoses of different sizes are used to fill a pool. The smaller hose can fill the pool in 1.5 times as long as the larger hose. If both hoses

are used it takes 9 hours to fill the pool. If only the larger hose is used, how many hours will it take to fill the pool?

User Autoboxer
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1 Answer

7 votes

Answer:

15

Explanation:

Let x represent the number of hours it takes the larger hose to fill the pool. Then each hour, it contributes 1/x of the pool volume. Similarly, the other hose contributes a volume of 1/(1.5x) each hour.

The two hoses together contribute a volume of 1/9 of the pool volume each hour:

1/x +1/(1.5x) = 1/9

2.5/(1.5x) = 1/9 . . . . combine the fractions

22.5/1.5 = x . . . . . . multiply by 9x

15 = x

It takes the larger hose 15 hours to fill the pool alone.

User Hazzik
by
8.3k points
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