An inlet pipe on a swimming pool can be used to fill the pool in 18 hours The drain pipe can be used to empty the pool in 20 hours If the pool is one-third filled and the inlet pipe drain are opened?

Hose A fills 1/3 of the pool per hour, hose B fills 1/4 of the pool per hour, and hose C fills 1/12 of the pool per hour.

Conveniently, these easily convey to 4/12, 3/12, and 1/12. So all three hoses together fill 4/12 + 3/12 + 1/12 = 8/12 (or 2/3) or of the pool per hour.

Therefore it takes one and one-half hours to fill the pool all the way. At the end of hour 1 the pool will be 2/3 of the way full, and since there's only 1/3 of the pool left to fill and our hoses can fill 2/3 of it per hour, we only need to run them for half-an-hour to get the last 1/3.