A man runs his car out of gas thereby completely emptying his 16 gallon tank. He only has a 3, a 6, and a 11 gallon container (and fortunately a wagon to carry the containers in) in his trunk. He has nothing else in which he can carry gas. He walks a few miles to a gas station, and as luck would have it the gauge on the pump is broken so he can not use that to measure the fuel. He is in a pretty remote area with only one gas station for miles. Gas costs $3.09⁹, and he only has a $50. Using only the containers provided, and only walking once to and from the gas station, how can he get exactly 16 gallons of gas into his car?

First, construct a balance where the two smaller cans (empty) balance out with the largest one (empty), thus establishing the tare.  Next, fill the 11-gal tank.  From it, fill the 6-gal tank.  Then fill the 3-gal tank and empty it into the 11-gal tank.  This leaves 8 gal in the 11-gal tank and 6 gal in the 6-gal tank.  Now place the tanks on the balance.  Begin filling the 3-gal tank until it is balanced.  It should take exactly two gallons to do this which yields 8 gallons on each side of the balance.  Thus, 16 gallons.

Edited on September 24, 2007, 12:31 am

Posted by hoodat on 2007-09-24 00:29:44