A reservoir has two inlets that fill it in 10 hours and 15 hours, and an outlet that empties it in 12 hours. At 8 am the two inlets are opened on the empty reservoir. At 10 am the outlet is also opened by mistake and left open. At what time is the reservoir full?

Explanation

1. 01

   Inlets together: $\frac{1}{10} + \frac{1}{15} = \frac{1}{6}$ per hour; in 2 hours $\frac{1}{3}$ is full.

2. 02

   With the outlet: $\frac{6 + 4 - 5}{60} = \frac{5}{60} = \frac{1}{12}$ per hour.

3. 03

   The remaining $\frac{2}{3}$ takes $\frac{2}{3} \times 12 = 8$ hours.

4. 04

   Full at 10 am + 8 hours = 6 pm.