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Ken's Puzzle of the Week

Slow Cows

Freddie the farmer has a paddock that he uses to graze his stock of cows.
Each cow eats the same amount of grass each day, regardless of how many other
cows are in the paddock and irrespective of the amount of grass left in the
paddock. In an experiment, Freddie puts 6 cows into the paddock and he finds out
it takes 3 days for them to eat all the grass. These 6 cows are then taken out
of the paddock to allow the grass to grow back.

After the grass has been allowed to grow back to the original amount, Freddie
then puts 3 cows into the paddock. This time he finds that it takes 7 days for
the 3 cows to eat all the grass in the paddock. Freddie is puzzled that the cows
took this long and consults a mathematician.

Freddie said "Geez mate, I dunno why me cows took that long to eat me paddock."

Marvin the mathematician replies "Well Freddie, tell me what assumptions you
made."

Freddie replies "Well mate, maybe me cows got sick or somethin', cos I reckon
that me 3 cows should have taken 6 days to eat me paddock, not 7 days! "

Marvin Replies, "I doubt that very much Freddie!"

After a while Marvin does some calculations and reveals that Freddie had
overlooked an important assumption. What was the assumption Freddie had
overlooked? Using Marvin's assumption, how long would a single cow take to
eat the same paddock?

Source: Reader Ben Nie. Bonus problem for homework.

Solution

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