A tank can be filled by one tap in 2 hours, while another tap can drain the tank in 3 hours. If both taps are opened simultaneously, how long will it take to fill the tank?

Explanation

The rate of filling by the first tap is 1/2 tank per hour, and the rate of emptying by the second tap is 1/3 tank per hour. The combined net filling rate is (1/2 - 1/3) = 1/6 tank per hour. Therefore, the time required to fill the tank when both taps are open is 6 hours.