Two inlet pipes can fill a tank in 20 minutes and 24 minutes respectively, while an outlet pipe drains water at a rate of 3 gallons per minute. If all three pipes operate simultaneously and the tank fills in 15 minutes, what is the total capacity of the tank?

Explanation

The combined filling rate minus the emptying rate equals the net filling rate. The rate of the waste pipe per minute is calculated as 1/15 - (1/20 + 1/24) = -1/40. Since the waste pipe removes 3 gallons each minute, one part (1/40 of the tank) corresponds to 3 gallons. Therefore, the total tank capacity is 3 × 40 = 120 gallons.