Pipes A and B can fill a tank individually in 12 minutes and 15 minutes, respectively. A third pipe, C, drains water at a rate of 45 liters per minute. When all three pipes are open simultaneously, the tank fills in 15 minutes. What is the total capacity of the tank?

Explanation

The combined filling rate of pipes A and B is 1/12 + 1/15 = 9/60 liters per minute. Let the draining rate of pipe C be 45 liters per minute, so its filling rate in tank units is 1/x where x is the capacity divided by 45. Using the equation (1/12) + (1/15) - (45 / capacity) = 1/15, solving for capacity gives 540 liters.