How many goats to eat all the grass ..............

[Gizmonster]

You need to clear a field of grass, and you've chosen to use an army of goats. Keep in mind that the grass is always growing, even as it is being eaten.

If you set 120 goats loose, the field will be cleared in 30 days.
If you set 48 goats loose, the field will be cleared in 90 days.
If you want the field cleared in 16 days, how many whole goats do you need? (I ask how many whole goats - 'cos the answer is not a whole number, so you'll need to round it up).

[pulse876]

Suppose the amount of grass initially on the field is G and suppose it grows at a rate of g per day. Also suppose each goat eats an amount of grass e per day.

If it takes 120 goats to clear the field in 30 days then:
120*30e = G + 30g, ie 3600e = G + 30g

If it takes 48 goats to clear the field in 90 days then:
48*90e = G + 90g, ie 4320e = G + 90g

So 720e = 60g, ie g = 12e

Hence G = 3600e � 30*12e = 3240e

To clear the field in 16 days requires n goats where:
n*16e = G + 16g, ie n*16e = 3240e + 16*12e = 3432e

So n = 3432/16 = 214.5, ie 215 goats.

[Gizmonster]

Spot on :o)

I was hoping it would take a bit longer for someone to solve ..... but there's always one smart ass lol >.<