A pipe can fill a petrol tank in 20 hours, but a leak in the tank can empty a…

Concept: when a fill source and a leak act on a tank together, compare their standalone rates — the fraction of the tank each moves per hour on its own. If the leak's standalone rate is larger than the fill's standalone rate, the two effects do not add up to a filling outcome: the tank net-drains, and the time to go from full to empty is the reciprocal of the net (leak minus fill) rate.

Application:

1. Pipe's own rate: it fills the whole tank alone in 20 hours, so its rate is 1/20 tank per hour.

2. Leak's own rate: a full tank alone drains through the leak in 15 hours, so its rate is 1/15 tank per hour.

3. Compare the two rates: 1/15 is larger than 1/20, so the leak removes tank-content faster than the pipe supplies it.

4. Net rate when both act together = leak rate minus fill rate = 1/15 - 1/20 = (4 - 3)/60 = 1/60 tank per hour, directed toward emptying.

5. Time for a full tank to become completely empty at this net rate = 1 divided by (1/60) = 60 hours.

Cross-check: over 60 hours the pipe alone would add 60/20 = 3 tank-equivalents while the leak alone would remove 60/15 = 4 tank-equivalents; the net removed is 4 - 3 = 1 full tank, matching a full tank running down to empty.

So the tank, starting full, becomes completely empty in 60 hours.