A pipe starts filling an empty tank at 8:00 a.m. and on its own would fill it in 9 hours. At 11:00 a.m. a crack opens in the base which by itself would drain a full tank in 18 hours, and it is not repaired. When does the tank fill?

Take the tank as 18 units: the pipe gives 2 units an hour, the crack takes away 1. In the three clean hours to 11:00 a.m. the pipe puts in 6 units, leaving 12. After that the net gain is 1 unit an hour, so 12 more hours are needed — the tank fills at 11:00 p.m. 5:00 p.m. ignores the crack. 2:00 a.m. treats the crack as present from 8:00 a.m. (18 hours at 1 unit an hour). 8:00 p.m. subtracts the times rather than the rates, taking 18 − 9 = 9 hours as the time still needed after 11:00 a.m.