Answer to Question #100472 in Physics for Katerina

Question

Suppose you have a grassy field, and cows eat grass at a constant rate.
Keep in mind, the grass keeps growing continuously.

48 cows can clear all the grass off the field in 90 days.

120 cows can clear all the grass off the field in 30 days.

How many cows would be needed to clear all of the grass in 16 days?
Round up to the nearest whole cow.

Answer 1

The initial amount of grass: i.

A cow eats a certain amount of grass in one day, call it c.

The field grows by a certain amount each day, call it g.

$$i + 90 g - 48(90 c)= 0\to i + 90 g - 4320 c = 0$$

$$i + 30 g - 30(120 c )= 0\to 1.2 i + 36 g - 4320 c = 0$$

$$0.2 i - 54 g = 0\to i=270 g$$

Thus,

$$270g + 30 g - 30(120 c )= 0$$

$$g=12c$$

It takes 12 cows to eat one day's growth in one day.