Tap P can fill a cistern in 6 hours and tap Q can empty the full cistern in 10 hours. If both taps P and Q are kept open simultaneously, then in how many hours will the empty cistern be completely full?

Using the net work rate formula, tap P fills the cistern at 1/6 per hour and tap Q empties it at 1/10 per hour. When both taps are open simultaneously, the net filling rate is 1/6 - 1/10, which equals 5/30 - 3/30 = 2/30 or 1/15 of the cistern per hour. Inverting this net rate gives the total time required to fill the empty cistern, which is 15 hours.

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