Three pipes, A, B, and C, are connected to a tank. Pipe A can fill the tank in 5 hours, pipe B in 6 hours, while pipe C can drain the tank completely in 12 hours. If all three pipes operate simultaneously, how long will it take to fill the tank?

Explanation

The combined filling rate per hour is the sum of the rates of pipes A and B minus the emptying rate of pipe C: (1/5) + (1/6) - (1/12) = 17/60 of the tank per hour. Therefore, the time to fill the tank is the reciprocal, 60/17 hours, which equals 3 hours and 9/17 of an hour.