Feeding frenzy
If it takes 6 cows 3 days to eat a field of grass and it takes 3 cows 7 days to do the same, how many days would it take 1 cow to do it?
Labels: mathemagic
posted by Chris at
3:42 PM
Friday, October 16, 2009
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10 Comments:
In reality, the grass will not grow very much in 3 days.
In seven days the grass might grow enough to keep growing enough that it may keep up with the grazing.
For one cow, the cow probably can't keep up with the grass.
Maybe your not a rancher.
There's nothing in the problem that should cause you to believe that I'm not a rancher.
Grass grows, cows eat the grass, grass grows. One of the main objectives in my business is call "prescribed grassing". Over grazing is difficult to rebound from.
The ToM presented suggests itself like 6 painters can paint 10 houses.. etc. etc.
But overgrazing is suggested here, and it is a serious condition. It causes the loss of topsoil thru erosion, and that may take thousand of years to recover.
With a carfully planned grazing plan, a herd may graze indefinately. Any rancher would horrified by the situation. But we can forgive a non-rancher for the posting.
I was using them as lawnmowers :)
Forget overgrazing.
In 3 days the field provides 18 cow-days.
In 7 days it provides 21 cow-days.
This would seem to suggest that the grass grows at the rate of 0.75cow-days per day.
Therefore, working backwards, the field would have 15.75 cow-days of grass at the start.
Adding 0.75 per day to this the single cow should then run out of feed after 63 days.
(I thought you would have structured this problem to make the answer 42 days. Maybe you did, and my reasoning was wrong!).
Hi Wiz. You got it - 63 days. You must have ESP: I nicked the problem from elsewhere and couldn't be bothered to re-work it for 42 days. But it had crossed my mind :)
for the 6 cows 3 days...1 cow will take 18 days and the 3 cows 7days 1 cow will take 21 days
Raisah. See the Wizard of Oz's solution - it is correct.
21days
The answer is 63, why post a wrong answer (especially without reasoning) after the right answer has been published and acknowledged?
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