What is the Cow Grazing Problem? Cattle grazing problems

A pasture is overgrown with grass, and the cattle are grazing and the grass is growing at a constant rate, and 27 cows can eat all the grass on the pasture in 6 days; It takes 9 days for 23 cows to eat all the grass in the pasture, but if 21 cows come to eat, how many days will they eat?

Answer This kind of problem is called: Newton's problem Complete solution idea: Assuming that the amount of grass eaten by each cow per day is 1, then the amount of grass eaten by 27 heads for 6 days is 27 6=162;The amount of grass eaten by 23 cows in 9 days is 23 9 = The difference between 162 and 162 is (9-6) days of newly grown grass, so the amount of new grass 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, the sum of the new grass grown in these 6 days is 15 6 = 90, so it can be seen that the original amount of grass in the pasture is 162-90 = 72 The new grass grows every day in the pasture is enough for 15 cows to eat for one day, and every day 15 of the 21 cows eat the newly grown grass. The remaining 21-15 = 6 (heads) exclusively eat the original grass.

So the grass on the pasture is enough to eat 72 6 = 12 (days), that is, the grass on this pasture is enough for 21 cattle to eat for 12 days.

Composite formula: [27 6-(23 9-27 6) (9-6) 6] [21-(23 9-27 6) (9-6)] = 12 (days).

I remember reading in a book: "The problem of cows eating grass is the problem of catching up, and the problem of cows eating grass is an engineering problem." "The first half of the sentence is very easy to understand, and when I tell the child, I also talk about it according to the idea of chasing the problem.

As for the second half of the sentence, it was not understood until last week.

A pasture in Xiaojun's house is overgrown with grass, and the grass grows at a uniform rate every day, and this pasture can feed 10 cows for 20 days and 12 cows for 15 days. If Xiaojun's family has 24 cows, how many days can they eat?

Answer. Grass speed: (10 20 12 15) (20 15) = 4

Lao Cao (distance difference): According to: distance difference = speed difference and catch-up time.

10 4) 20=120 or (12 4) 15=120

Catch-up time = distance difference Speed difference: 120 (24 4) = 6 (days).

One pasture can feed 58 cows for 7 days, or 50 cows for 9 days. Assuming that the amount of grass grows equally every day, and the amount of grass eaten by each cow is also equal, how many cows can eat for 6 days?

Answer. Grass speed: (50 9 58 7) (9 7) = 22

Old grass (poor distance): 50 22) 9=252 or (58 22) 7=252

Finding a few cows is to find the speed of the cow, the speed of the cow = the distance difference and the time of catching up with the grass speed 252 6 22 = 64 (head).

Newton's problem: The problem of cattle grazing or the problem of growing and waning.

There is a pasture that grows at a rate every day, and this pasture can feed 17 cows for 30 days and 19 for 24 days.

Now a number of cows are grazing, after 6 days, 4 cows are sold, and the remaining cattle eat the grass for 2 days.

Solution: Let a cow eat grass a day.

17 cows grazing for 30 days: 17 30 = 510 (portions) 19 cows grazing for 24 days: 19 24 = 456 (portions) The grass grows every day:

510-456) (30-24) = 9 (parts) There was grass in the meadow: 510-9 30 = 240 (parts) There were x cows.

6x+2(x-4)=240+9 (6+2): x=40

It turned out to be 40 cows.

Suppose the grass that a cow eats in a day is the unit "1".

Then the grass that grows every day is [21*8-24*6] [8-6]=12 units, and it turns out that there is grass is 24*6-6*12=72 units.

To never finish eating, that is, the amount of grass eaten every day is equal to the amount of growth, that is, to:

12 1 = 12 cows.

Equation solution: Let the pasture have a grass amount x, the grass grows y every day, and each cow eats a certain amount of grass per day (x+6y) (24*6)=(x+8y) (21*8)(x+6y) 6=(x+8y) 7

x=6y, set a maximum of m cattle pasture, and never finish the pasture.

x+6y)/(24*6)=y/m

12y/(24*6)=y/m

m=12 (only).

If 13 cows eat for five days, this is not an even possible situation: 3 cows eat for 20 days and 12 cows eat for 5 days, which is satisfied without counting the grass growth (the grass growth is 0).

What's more, if there are 13 cows, one more cow will definitely not be enough to eat (unless the grass is negative), and the denominator of the formula you give is 20-4 days wrong.

First of all, your question itself is unreasonable, 13 cows eat for 5 days, assuming that the cows eat grass at a rate of 1, then the cows eat (13 5 1) units of grass, that is, 65 units of grass. Then 3 cows ate 60 units of grass for 20 days, but on the 5th day there were 65 units of grass, why did they only have 60 units of grass on the 20th day? Unless the grass is ruined, so it grows negatively.

And you wrote the title incorrectly, it was eaten by 4 cows, and it was eaten in 13 days. Not 13 cows to eat, 4 days to eat)

Cow eating grass is a very traditional classic primary school Olympiad problem, if you want to quickly analyze cattle and grass, it is actually very simple.

Mainly grasp the analysis of "change" and "unchanged", in the cow grazing, the grass can be divided into the old grass (that is, the grass that already exists, this part can be considered unchanged) and the new grass (that is, all the grass that grows by the last day), in addition to the speed of the grass that grows every day and the speed of the cow eating grass, I hope to satisfy you through the example of the problem of cows eating grass

Example 1: A pasture in Xiaojun's house is overgrown with grass, and the grass grows at a uniform rate every day, and this pasture can feed 10 cows for 20 days and 12 cows for 15 days. If Xiaojun's family has 24 cows, how many days can they eat?

Solution: 1. Grass speed: (10 20 12 15) (20 15) = 42, old grass (original grass):

According to: old grass = (number of cattle - grass speed) days (10 4) 20 = 120 or (12 4) 15 = 1203, edible days = old grass (number of cattle - grass speed).

120 (24 4) = 6 (days).

What do you think? Do you understand?

I hope my analysis is helpful to you.

Newton's problem: The problem of cattle grazing or the problem of growing and waning.