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Pasture Puzzles (Posted on 2013-11-01) Difficulty: 3 of 5

See Slow Cows

(a) More Slow Cows.

If 14 cows take exactly 5 times as long to graze out a pasture as 54 cows, and 38 cows take exactly 5 times as long as 174 cows, what is the largest prime number of cows that can graze the same pasture?

Note 1: In this part, all times are calculated in exact whole numbers of days, and the pasture is of the smallest size compliant with the given conditions.

(b) Newton's Goats

Six goats eat all the grass in a pasture in exactly three days, while 3 goats take exactly seven days to graze out the same pasture. On what day will the pasture become exhausted, if two goats are grazing there?

Note 2: In both parts, the grass grows at a steady rate, and each animal eats the same, constant, amount each day; but, unlike cows, goats eat grass down to the stubble, so that areas that have already been grazed do not resume growth while the pasture remains in use.

See The Solution Submitted by broll    
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re(4): Solution | Comment 8 of 10 |
(In reply to re(3): Solution by broll)

Dear Broll,

Sorry got the second part its similar to the prediction of EMI for a housing loan. Wherein the interest on loan is like the rate of growth of pasture and initial principle in the amt of grass in pasture to start with. The EMI's should be such that at the end of the days the principle left is zero. But this is more trial and error kind of problem especially if the no of days is large. Hope I am right this time.


  Posted by Salil on 2013-11-07 04:45:12
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