A cistern has two inlets, which fill it in 15 minutes and 10 minutes, and one outlet. With all three open, the empty cistern fills in 18 minutes. How long would the outlet alone take to empty the full cistern?

Explanation

1. 01

   Inlets together: $\frac{1}{15} + \frac{1}{10} = \frac{2+3}{30} = \frac{1}{6}$ per minute.

2. 02

   Outlet = inlets − net = $\frac{1}{6} - \frac{1}{18} = \frac{3-1}{18} = \frac{2}{18} = \frac{1}{9}$.

3. 03

   The outlet empties it in 9 minutes.