A man had a 10-gallon keg full of wine, and an empty jug. On Monday he drew off a jugful of wine and filled up the keg with water. On Friday, after the wine and water had been thorougly mixed, he drew off another jugful and again filled up the keg with water. The keg then contained equal quantities of wine and water.

What was the capacity of the jug?

Let w be the fraction of wine left after taking out the first jug. Then the fraction of wine left after taking out the second jug is w^2=1/2, so that w=1/sqrt(2). Hence the jug holds 10*(1-w)=2.92893219... gallons.

Posted by Richard on 2004-07-14 13:36:47