There is a leak in the bottom of a cistern. When the cistern had no leak, it was filled in 9 hours. It now takes an hour longer. If the cistern is full of water, then how long would it take in leaking itself empty?

Using the net work formula, the filling pipe's rate is 1/9 of the cistern per hour, while the net filling rate with the leak is 1/10 per hour. The leak's emptying rate is the difference between these two rates, which is 1/9 - 1/10 = 1/90 of the cistern per hour. Therefore, acting alone at this rate, the leak would take 90 hours to empty the full cistern.

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