Posted by Heidi on Tuesday, November 2, 2010 at 4:14pm.
A singleengine airplane carries enough fuel for an 8hour 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?

Algebra  MathMate, Tuesday, November 2, 2010 at 6:08pm
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.
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