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?
Assume the jug IS 2.92 gallons. Mathmatically we should be able to prove after Friday we would have a 50/50 mix of wine and water.
After Monday, we would replace 2.92 gallons of wine with 2.92 gallons of water. this gives us a mix 70.7% wine, 29.3% water.
This will be the ratio of the mix going into the jug on Tuesday. 70.7% of 2.92 gallons is 2.07 gallons. Add this to the wine we took out on Monday, we have now lost 4.99 gallons. (pretty much the 50/50 mix we are shooting for on Friday.
WEDNESDAY - 50% of 2.92 gallons is 1.46 gallons of wine lost, bringing the mix ratio to 35.4%.
THURSDAY - 35.4 % of 2.92 gallons is 1.03 gallons of wine lost, bringing the mix down to 25.0% wine.
FRIDAY - we have already lost 7 1/2 gallons of wine by this point. 25% of 2.92 is .73 gallons lost, bringing the grand total of 8.23 gallons of wine lost this week, making the mix only 17.7% wine.
Use this logic with a 1/2 gallon jug and you will lose just over the 5 gallons total we are shooting for. I stick with my .43 gallon jug.
2.92 doesn't work
