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Subj:.....Jack Sprat And His Wife (S643)           From the book              "More Mathematical Puzzles                 of Sam Loyd"            Edited by Martin Gardner            From: Dover Publications in 1960 Drawing of Jack Sprat amd his wife from Chron.com   How long would it take Jack Sprat and his wife to eat a barrel of mixed pork, half fat and half lean? According to Mother Goose, Jack Sprat could eat no fat and his wife could eat no lean. Together they could eat a barrel if fat pork in sixty days, whereas it would take Jack thirty weeks to perform this feat alone. Together they consume a barrel of lean pork in eight weeks, although his wife alone could not dispose of it in less than forty weeks. Assume that Jack would always eat lean pork whenever it was available and that his wife would do the same with fat, how long would it take both of them to eat a barrel of mixed pork, half fat and half lean? . . Finger pointing down from darrell94590 on 1/2/2006 .   Drawing from Ripleys-Believe It Or Not ..               THE SOLUTION   From the facts given we can conclude that Jack eats lean pork at a rate of 1 barrel in 10 weeks, therefore he would finish the half-barrel of lean in 5 weeks.  During this same period, his wife (who eats fat at a rate of 1 barrel in 12 weeks) would consume 5/12 of a barrel of fat.  This would leave 1/12 of a barrel of fat for both of them to eat at a rate of 1 barrel in 60 days.  They would finish the fat in five days, so the total amount of time would be 35 days plus 5 days, or 40 days altogether.

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