A tank is filled by three pipes, each delivering water at a constant rate. When the first two pipes work together, they fill the tank in the same amount of time that the third pipe takes to fill it alone. The second pipe fills the tank 5 hours quicker than the first pipe, but 4 hours slower than the third pipe. How long does the first pipe take to fill the tank by itself?

Explanation

Let the first pipe fill the tank in x hours. Then, the second pipe takes (x - 5) hours, and the third pipe takes (x - 9) hours to fill the tank alone. According to the problem, the combined rate of the first two pipes equals the rate of the third pipe: 1/x + 1/(x - 5) = 1/(x - 9). Solving this equation yields x = 15 hours, which is the time taken by the first pipe.