Two taps fill a tank in 10 and 12 minutes, and an outlet empties it in 15 minutes. All three are opened on an empty tank. How long does it take to fill?

Explanation

1. 01

   Net rate $= \frac{1}{10} + \frac{1}{12} - \frac{1}{15} = \frac{6 + 5 - 4}{60} = \frac{7}{60}$ of the tank a minute.

2. 02

   Time $= \frac{60}{7}$ minutes, about 8.6 minutes.