Cows are pastured at some grassland.
When 6 cows are pastured, grasses are eaten up in 30 days.
When 10 cows are pastured, grasses are eaten up in 12 days.
At this time, answer the next questions.
Noted that grasses grow at a fixed rate every day in this grassland.
In addition the amount of the grass each cow eats per day is same.
(1) Find the number of cow to be pastured without the grass of the grassland being eaten up.
(2) How many cows at least should be pastured in order to eat all the grass of the grassland within six days?
Answer
(1) Three
(2) 17
Solution
(1) The amount of the grass that one cow eats in a day is assumed to be one.
The amount of the grass growing in this grassland per day is （180 - 120）/（30 - 12） = 10/3.
According to 1 × 3 < 10/3 and 1 × 4 > 10/3, the number of cow to be found is three.
(2) The total amount of the grass grown in this grassland, 180 - 10/3 × 3 = 80.
80 / 6 = 40/3
(40/3) + (10/3) = 50/3 = 16.66---
Therefore the number of cow at least is 17.
