Pumping alone at their respective constant rates, one inlet pipe fills an empty tank to $\displaystyle \frac { 1 }{ 2 } $ of capacity in 3 hours and a second inlet pipe fills the same empty tank to $\displaystyle \frac { 2 }{ 3 } $ of capacity in 6 hours. How many hours will it take both pipes, pumping simultaneously at their respective constant rates, to fill the empty tank to capacity?

The first pipe fills 1/2 of the tank in 3 hours, so its rate is 1/6 of the tank per hour. The second pipe fills 2/3 of the tank in 6 hours, so its rate is 1/9 per hour. Their combined rate is 1/6 + 1/9 = 5/18 per hour, so the time to fill the tank is 18/5 = 3.6 hours.

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