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A Keg of Wine (Posted on 2004-07-14) Difficulty: 3 of 5
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?

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (5 votes)

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Hints/Tips re(3): I just read the question correctly | Comment 17 of 27 |
(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

  Posted by SilverKnight on 2004-07-15 13:30:27

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