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?
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.