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?

(In reply to re(2): I just read the question correctly by Jim)

Start: 10 gallons of wine, 0 water

After Jug 1: 9.57 gallons of wine, .43 gallons water

After Jug 2: 9.57 - (.43)(.957) = 9.15489 gallons of wine

After Jug 3: 9.15489 - (.43)(.915489) = 8.764675 gallons of wine

After Jug 4: 8.387794 gallons of wine

After Jug 5: 8.027119 gallons of wine

........Down to the 16th, which takes you just below 5 gallons of wine. Logically with a 0.43 gallon jug you cannot remove more than 2.15 gallons of wine. On a five-day schedule, you would need about a 1.2945 gallon jug.

Posted by Eric on 2004-07-15 13:35:45