Pipe A can fill a tank in 6 hours. However, due to a leak at the bottom, it now takes 9 hours to fill the tank with the pipe running. How long will it take for the leak alone to drain the full tank?

Explanation

Let the time taken by the leak to empty the tank be x hours. The filling rate of the pipe is 1/6 tank per hour, and the effective filling rate with the leak is 1/9 tank per hour. Therefore, the leak's emptying rate is 1/x. Using the equation: 1/6 - 1/x = 1/9, we get 1/x = 1/6 - 1/9 = (3 - 2)/18 = 1/18. Hence, x = 18 hours.