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Grazing cows


Best Answer plasmid, 07 November 2013 - 04:41 AM

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#1 BMAD

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Posted 04 November 2013 - 01:36 AM

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?

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#2 mattil

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Posted 06 November 2013 - 07:14 AM

Spoiler for Was it maybe...


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#3 BMAD

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Posted 06 November 2013 - 01:27 PM

nope.  that assumption was safely given.


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#4 harey

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Posted 06 November 2013 - 03:45 PM

Spoiler for


Edited by harey, 06 November 2013 - 03:46 PM.

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#5 BMAD

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Posted 06 November 2013 - 11:50 PM

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I agree that you found the 'missed assumption' by the farmer but i calculated a different answer.  Someone please verify.


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#6 plasmid

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Posted 07 November 2013 - 04:41 AM   Best Answer

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Edited by plasmid, 07 November 2013 - 04:46 AM.

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#7 harey

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Posted 07 November 2013 - 09:14 AM

The first part did not require much calculation ;). As usually, I made an arithmetic error. I tried with b=60, c=80 - plasmid is correct.


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#8 BMAD

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Posted 07 November 2013 - 02:42 PM

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this is what i have as well.


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#9 DeGe

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Posted 08 November 2013 - 12:17 PM

You assume a constant rate of growth of grass over the entire duration.

I'm not sure about this and pls correct me if I am wrong: If some grass is eaten on any given day, shouldn't the rate of growth of grass be slower the next day?


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#10 BMAD

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Posted 08 November 2013 - 09:53 PM

You assume a constant rate of growth of grass over the entire duration.

I'm not sure about this and pls correct me if I am wrong: If some grass is eaten on any given day, shouldn't the rate of growth of grass be slower the next day?

 

i think the rate would be the same in terms of average growth


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