Question

One pump fills a tank in 20 hours and another in 15 hours. When a third pump is added the tank fills in 6 hours. Find out how long it takes the 3rd pump to fill the tank alone.

Answer 1

Every hour, the first pump fills 1/20 of the tank, and the second fills 1/15 of the tank.  If, when combined with the third pump, all three pumps fill 1/6 of the tank in an hour, the third pump fills 1/6-1/15-1/20=$\frac{1}{20}$ of the tank every hour, so it takes a total of 20 hours to fill the tank alone.