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 ?

Let c = daily ration of a cow.

r = daily rate of growth of grass in the pasture

I = initial amount of grass in the pasture

Then, by the problem,

I + 40r = 1600c

I + 60r = 1800c, giving:

r = 10c, so that: I = 1600c - 40r = 1200c

Let the number of days that the pasture would be able to support 20 cows be d.

Then, we must have:

I + dr = 20dc

or, 1200c = 20dc - 10dc, giving:

d = 1200/10 = 120

Consequently, the pasture would be able to support 20 cows for

120 days