A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time in which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The

Question

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time in which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:

Accepted Answer

15 hours. Let the first pipe take $x$ hours, so the second takes $x-5$ hours and the third takes $x-1$ hours. Since the first two together fill the tank in the same time as the third alone, $\frac1x+\frac1{x-5}=\frac1{x-1}$. Solving gives $x=15$ hours.

Solution

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