S = Start blades of grass (blades)
g = grow rate (blades/day)
e = cow eating rate (blades/day)
n = number of cows
d = number of days

The General formula in 'Blades of Grass' units: S + dg - nde = 0

Inserting the values given for the two examples:
S + 24g - 70 * 24 e = 0
S + 60g - 30 * 60 e = 0

From e = (S + 24g) / (70 * 24) = (S + 60g) / (30 * 60), S = 480g.
Putting 480g back into the two examples, then e = 3g/10.

The formula for the problem is: S + 96 g - Cn 96 e = 0
Inserting for S and e:
480g + 96g = Cn * 96 * (3g/10), and Cn = 20.

It will take twenty cows to eat all the grass in 96 days!
 
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Nov 17, 2008