A pasture is covered with grass, cows are eating grass, and the grass grows at a constant speed. 27 cows can eat all the grass in the pasture in 6 days; It will take 23 cows 9 days to finish all the grass in the pasture. How many days will it take if 2 1 cow comes to eat?

answer

This kind of problem is called: the complete solution of Newton's problem: suppose that the daily grazing amount of each cow is 1, and the grazing amount of 27 cows in the first six days is 27× 6 =162; The grazing amount of 23 cows in 9 days is 23×9=207. The difference between 207 and 162 is grass newly grown in (9-6) days, so the amount of grass newly grown in the pasture every day is (207-162) ÷ (9-6) =15. Because the amount of grass eaten by 27 cows in 6 days is 162, they are newly grown in these 6 days. Therefore, it can be seen that the original grazing amount of this pasture is 162-90=72. The newly grown grass in the pasture is enough for 15 cows to eat for one day. Let 2 1 5 cows eat the newly grown grass every day, and the remaining 21-15 = 6 (head). So the grass on the pasture is enough to eat 72÷6= 12 (days), that is, the grass on this pasture is enough to eat 2 1 cow 12 days.

Comprehensive formula: [27× 6-(23× 9-27× 6) ÷ (9-6) ÷ [21-(23× 9-27× 6) ÷ (9-6)] = 65438.

The problem of cattle grazing is a kind of difficult problem in primary school Olympic Mathematics. I remember reading in a book: "The problem of cattle grazing is catching up, and the problem of cattle grazing is an engineering problem." The first half of the sentence is easy to understand. When I tell my children, I also follow the train of thought of chasing questions. I didn't understand the latter part until last week.

2.

A pasture of Xiaojun's family is covered with grass and grows at a constant speed every day. This pasture can feed 10 cows for 20 days, 12 cows 15 days. If Xiaojun keeps 24 cows, how many days can he eat?

answer

Grass speed: (10× 20-12×15) ÷ (20-15) = 4.

Old grass (distance difference): according to: distance difference = speed difference × catch-up time

(10-4) × 20 = 120 or (12-4) ×15 =120.

Catch-up time = distance difference ÷ speed difference: 120 ÷ (24-4) = 6 (days)

3.

A pasture can feed 58 cows for 7 days, or 50 cows for 9 days. Assuming that the grass grows equally every day and each cow eats the same amount of grass, how many cows can eat for 6 days?

answer

Grass speed: (50× 9-58× 7) ÷ (9-7) = 22.

Old grass (distance difference): (50-22) × 9 = 252 or (58-22 )× 7 = 252.

Finding a few cows means finding the speed of cattle, which is equal to the distance difference, the chasing time, and the grass speed is 252 6+22 = 64 (head).