Pipe A can fill a tank in 10 hours and pipe B in 15 hours. Pipe C can empty the full tank in 12 hours. If all three are opened together, how long…

Work per hour (fraction of the tank): A fills \(\tfrac{1}{10}\), B fills \(\tfrac{1}{15}\), C empties \(\tfrac{1}{12}\).

\(\dfrac{1}{10} + \dfrac{1}{15} - \dfrac{1}{12} = \dfrac{6 + 4 - 5}{60} = \dfrac{5}{60} = \dfrac{1}{12}\)

So the tank fills at 1/12 per hour: 12 hours.

— rhs