Math and Arithmetic
Brain Teasers and Logic Puzzles

How much time will it take for two pipes that are opened at the same time to fill a tank if one will fill it when opened by itself in 36 hours and the other will fill it in 45 hours?

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October 03, 2007 4:41PM

The first pipe will fill one tank in 36 hours. Therefore in one hour it will fill 1/36 tanks. The second pipe will fill one tank in 45 hours. Hence in one hour it will fill 1/45 tanks. Between them, then, the two pipes will fill 1/36 + 1/45 tanks in an hour. This equals 5/180 + 4/180 = 9/180 = 1/20 tanks per hour. Hours per tank is just the reciprocal of tanks per hour, i.e. 1/[1/20] = 20 hours to jointly fill a tank. Incidentally, adding reciprocals and taking an overall reciprocal is a very commonly used trick. It is used to calculate net parallel resistance in electric circuits. Here, time to fill a tank (or resistance to tank-filling!) can be considered analogous to electrical resistance.