Time to fill a pool

Question

A child's pool can be filled in 20 minutes if two hoses are used. Used alone, the larger how can fill the pool 5 minutes faster than the smaller hose. To the nearest tenth of a minute, how long does it take the larger hose to fill the pool?

Answer 1

Let x = time (in minutes) for the smaller hose to fill the pool

 

    x-5 = time (in minutes) for the larger hose to fill the pool

 

1/x + 1/(x-5) = 1/20

 

Multiply by the LCD, 20x(x-5):  20(x-5) + 20x = x(x-5)

 

                              20x - 100 + 20x = x² - 5x

 

                              x² - 45x + 100 = 0

 

x = [45 ± √ 1625] / 2 = 42.7 or 2.3 

 

If x = 2.3, then x-5 is negative, which is impossible.

 

So, x = 42.7 min (time for the small hose)

 

Time for the large hose = x-5 = 37.7 min