There is a pasture where grass grows at a fixed rate every week.
If ten cows are kept since when grass has grown in the entire pasture, it takes sixteen weeks to be no grass in this pasture.
If fifteen cows are kept, it takes eight weeks to be no grass.
If twenty-five cows are kept, how many weeks does it take to be no grass?
If ten cows are kept since when grass has grown in the entire pasture, it takes sixteen weeks to be no grass in this pasture.
If fifteen cows are kept, it takes eight weeks to be no grass.
If twenty-five cows are kept, how many weeks does it take to be no grass?
Answer
Solution
When the volume of the grass which one cow eats in one week is set to 1, the volume of the grass which ten cows eat in 16 weeks is 1 × 10 × 16 = 160.
The volume of the grass which 15 cows eat in eight weeks is 1 × 15 × 8 = 120.
These difference of 40(160 - 120 = 40) is equal to the volume of the grass which has grown up in eight weeks (16 - 8 = 8).
Thus, the volume of the grass which growing up in one week turns out to be 5(40 / 8 = 5).
Then, the volume of the grass in this pasture first is 80(160 - 5 × 16 = 80).
When 25 cows are kept, the volume of grass which decreases in one week is 20(1 × 25 × 1 - 5 × 1 = 25 - 5 = 20).
Therefore, it takes 4 weeks(80 / 20 = 4).
Four weeks
When the volume of the grass which one cow eats in one week is set to 1, the volume of the grass which ten cows eat in 16 weeks is 1 × 10 × 16 = 160.
The volume of the grass which 15 cows eat in eight weeks is 1 × 15 × 8 = 120.
These difference of 40(160 - 120 = 40) is equal to the volume of the grass which has grown up in eight weeks (16 - 8 = 8).
Thus, the volume of the grass which growing up in one week turns out to be 5(40 / 8 = 5).
Then, the volume of the grass in this pasture first is 80(160 - 5 × 16 = 80).
When 25 cows are kept, the volume of grass which decreases in one week is 20(1 × 25 × 1 - 5 × 1 = 25 - 5 = 20).
Therefore, it takes 4 weeks(80 / 20 = 4).
