Question

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?

Answer 1

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.