Question

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?

Answer 1

Answer:

  15

Step-by-step 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.