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)
Jim,
It seems to stand to reason that the greater the number of jugs-worth
of wine/water mix drawn, the smaller the jug should be to achieve a
50/50 mix. But your answer is too small.
For 1 draw, it is the obvious 5 gallon jug.
For 2 draws, we see (from earlier solutions posted) that the answer is about... 2.92893 gallons.
For more draws, we would expect the size of the jug to diminish, and in
fact, I've run this numerically... and with 5 draws, we need a jug of
approximately 1.2945 gallons (not .43 gallons), to achieve a 50/50 mix at the end.
For more completeness:
for 3 draws the jug must be ~2.063 gallons, and
for 4 draws the jug must be ~1.591 gallons.
- SK
re(3): I just read the question correctly
