posted by Heidi .
A single-engine airplane carries enough fuel for an 8-hour flight. After the airplane has been flying for 1 h, the fuel tank begins to leak at a rate that would empty the tank in 12 h. How long after the leak begins does the plane have until it runs out of fuel?
The rest of the fuel can last 7 hours in flight, and will leak in 12 hours.
So each hour, the plane uses 1/7th of what's left, and leaks 1/12th of what's left, for a total of 19/84th of what's left.
It will therefore last 84/19 hours.