Question

Four hoses are filling a pool. The first hose alone would fill the pool in 4 hours while the second hose takes 6 hours. The third hose and the fourth hose each take 8 hours to fill the pool. How long would it take to fill the pool if all 4 hoses are turned on?

Answer 1

1 1/2 hours.

Explanation:

We work in fractions of the pool that the hoses can fill in 1 hour, and this gives us the equation:

1/4 + 1/6 + 1/8 + 1/8 = 1/x where x is the times taken by 4 hoses turned on.

LCD = 24x so, multiplying through by 24x, we get:

6x + 4x + 3x + 3x = 24

16x = 24

x = 1 1/2 hours.