Page 116 - NUMINO Challenge_D2

Basic Concepts Newton’s Method

The problem of finding the time it takes for a
cow to graze can be answered by using the
Newton’s method, which is named after Isaac
Newton. Newton’s method is different from
other general problems because it assumes
that the grass is growing every day.
If there is enough grass on the farm for two cows to graze during a five-day
period, one cow can graze more than ten days, since the grass is growing
every day. As above, you need to figure out how much grass grows every day
in order to solve problems using Newton’s method.

Example There is a ranch where the grass grows at the same speed every
day. If there are 8 cows, the amount of grass is enough for 6 days,
and if there are 6 cows, the amount of grass is enough for 10 days.
If the amount of grass that one cow eats in a day is 1, what is the
amount of grass that grows in a day on this ranch? (The amount of
grass that cows eat is the same every day, and every cow eats the
same amount of grass.)

Class Notes

If the amount of grass that one cow eats is 1, the amount of grass that 8 cows eat in 6 days is

86 , and the amount of grass that 6 cows eat in 10 days is 6 10 .

The difference between the amount of grass that feeds the cows for 10 days and the amount

of grass that feeds the cows for 6 days is the amount of grass that grows for 4 days.

Therefore, the amount of grass that grows in a day is ( )4 .

Try It Again In order to maintain a constant amount of grass on the ranch
from Example above, how many cows should be raised on the
ranch?

113Communication