On a certain pasture grass grows at a even rate. It is known that 40 cows can graze on it for 40 days before the grass is exhausted, but 30 cows can graze there as long as 60 days.

How many days would pasture last if 20 cows were to graze on it ?

(my first post - this is practise)

Let C be a cow-day - the amount of grass a cow eats in a day.
So,
a) In 40 days the field + 40 days growth supplies 1600C
b) In 30 days the field + 60 days growth supplies 1800C
Clearly the extra 20 days growth provides the extra 200C
From this we see that the field grows at a rate to feed 10 cows without depleting (200C/20)
There must therefore be 1200C worth of grass in the field (derived from either a) or b))which would take the extra 10 cows from the question 120 days to get through

Posted by Lee on 2003-08-27 01:53:11