Cows and growing Grass
Algebra
Level
3
It takes 24 days for 70 cows and 60 days for 30 cows to eat the whole of the grass in a farm. How many cows are needed to eat the grass in 96 days?
Assume that the grass are growing at a uniform rate.
The answer is 20.
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1 solution
G - initial grass in the farm
rg - rate at which grass grows / day
rc - rate at which one cow eats grass / day
n - no of cows that eat the grass in 96 days ?
We can form the following equations based on :-
initial grass + amount of growing = amount of grass consumed by cows
G + 24*rg = 70 * 24 * rc (1) (70 cows consumed the farm in 24 days)
G + 60*rg = 30 * 60 * rc (2) (30 cows consumed the farm in 60 days)
G + 96*rg = n * 96 * rc (3) (n ?? cows consumed the farm in 96 days)
subtracting (2) - (1)
(60 * rg) - (24 * rg) = (30 * 60 * rc) - (70 * 24 * rc)
36 * rg = 120 * rc (4)
Subtracting (3) - (2)
(96 * rg) - (60 * rg) = (n * 96 * rc) - (30 * 60 * rc)
36 * rg = (n * 96 - 30 * 60) * rc
120 * rc = (n * 96 - 30 * 60) * rc (5)
substitute from eq. (4) in (5) we get
120 = (n * 96 - 1800)
n = 20 cows