A tank that normally fills in 9 hours takes 10 hours to fill due to a leak at the bottom. If the tank is full, how long will it take for the leak alone to empty it?

Explanation

Let the time taken by the leak to empty the tank be x hours. The filling rate is 1/9 tank per hour, and with the leak, the effective filling rate is 1/10 tank per hour. The leak's emptying rate is therefore: (1/9) - (1/x) = 1/10 Solving for x: 1/x = 1/9 - 1/10 = (10 - 9)/90 = 1/90 Hence, x = 90 hours.