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the cow

 
 
Reply Sat 5 Nov, 2005 10:53 am
A cow can eat a third of the grass in a field in 3 days and the fourth
of grass in the same field in 2 days. How long will it take to eat the
entire grass.


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Type: Discussion • Score: 1 • Views: 939 • Replies: 14
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Chai
 
  1  
Reply Sat 5 Nov, 2005 12:32 pm
10 days if you mean the cow could eat a 1/4 of the remaining grass in 2 days.
0 Replies
 
markr
 
  1  
Reply Sat 5 Nov, 2005 12:37 pm
approximately 26 days
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Merry Andrew
 
  1  
Reply Sat 5 Nov, 2005 01:31 pm
Well...grass grows back, y'know.
0 Replies
 
markr
 
  1  
Reply Sat 5 Nov, 2005 04:36 pm
I assumed the grass continues to grow until eaten.
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whimsical
 
  1  
Reply Sat 5 Nov, 2005 05:25 pm
"approximately 26 days"

Explain your answer please.
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Merry Andrew
 
  1  
Reply Sat 5 Nov, 2005 05:26 pm
Not necessarily. Why is Whimsical grinning ear to ear at the bottom of his post? Cows browse, they don't tear up the grass by the roots. And they don't browse that close to the ground, either. After a herd of cows has passed over a pasture, there's plenty left for sheep. I think this is a trick riddle.
0 Replies
 
markr
 
  1  
Reply Sat 5 Nov, 2005 05:32 pm
Merry Andrew wrote:
Not necessarily. Why is Whimsical grinning ear to ear at the bottom of his post? Cows browse, they don't tear up the grass by the roots. And they don't browse that close to the ground, either. After a herd of cows has passed over a pasture, there's plenty left for sheep. I think this is a trick riddle.

I may be wrong, but it was an assumption I made.
0 Replies
 
markr
 
  1  
Reply Sat 5 Nov, 2005 05:40 pm
whimsical wrote:
"approximately 26 days"

Explain your answer please.


I did this in Excel by approximating the growth and consumption of the grass in 1/100ths of a day. I tweaked the numbers to make the three-day consumption 4/3 of the two-day consumption. My final answer was a bit more than 26 days.
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markr
 
  1  
Reply Sat 5 Nov, 2005 06:43 pm
If the grass continues to grow after being eaten:
G = initial volume of grass (whole field)
g = volume of grass growth per day (whole field)
c = volume of consumed grass per day

2 days:
(G + 2g) / 4 = 2c
or
(i) G + 2g = 8c

3 days:
(G + 3g) / 3 = 3c
or
(ii) G + 3g = 9c (b)

subtract (i) from (ii) to get:
g = c
which means that the growth rate matches the consumption rate; so the field will never be completely consumed (unless I'm wrong).
0 Replies
 
Merry Andrew
 
  1  
Reply Sat 5 Nov, 2005 08:27 pm
I have a feeling you're not wrong, markr.
0 Replies
 
whimsical
 
  1  
Reply Sun 6 Nov, 2005 04:08 am
And so the answer is NEVER.
0 Replies
 
spidergal
 
  1  
Reply Sun 6 Nov, 2005 06:01 am
ok, (x/4)+(x/3) = 5, so, 7x/12 = 5. Then, x = (12*5)/7 = 60/7 = 8 4/7 days
0 Replies
 
bobrath
 
  1  
Reply Wed 4 Jan, 2006 12:41 am
12 days
0 Replies
 
bobrath
 
  1  
Reply Wed 4 Jan, 2006 12:43 am
Exactly 12 days
0 Replies
 
 

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