Will anyone solve the cow grazing problem ? Help, urgently

If the conditions you give are insufficient, I'm afraid you can't solve it, and you should give a different cow to eat for different days before you can solve it. Yes, if there are 2 conditions, yes.

Grass growth rate = (number of cows 1 * more days - number of cattle 2 * fewer days) (more days - fewer days).

The amount of original grass The number of cattle heads * the number of days eaten The growth rate of the grass * the number of days eaten;

Number of days eaten Original amount of grass * (number of cows, growth rate of grass);

Number of cattle head The amount of grass * the number of days eaten The growth rate of the grass.

It can be solved through the above 4 relationships.

A total of 30 cows.

Because the total amount of grass for 10 hectares is 12*25 (cow days) = 300

It is easy to know that 1 hectare of grass is 30 (cow days), that is, 30 cows eat a day.

12 cows can eat all the grass on 10 hectares of grassland in 25 days.

During this period, the grass grows non-stop, so the answer should be less than 30 cows.

In fact, the growth of forage grass will be affected by water, so it is difficult for us to determine a growth cycle of forage grass here In addition, only grass that has been eaten by cattle grows, and grass that has not been eaten (we say that it grows very little, which is negligible) At this time, you will find that if we take different grazing strategies, it will have different effects For example:

Scenario 1 Eat the grass that has been eaten until it is finished, and the grass that has not been eaten grows very little At this time, we assume that the growth efficiency of the grass in the whole grassland is a

Scenario 2Try to let the cow eat the grass that has not been eaten, and the amount of grass that has been eaten will be more than in case 1, so there will be more grass to grow

From the above, it can be seen that case 2 is more efficient than case 1, so case 2 will get more days than case 1

This question is really troublesome to analyze You see, this question will be related to the following factors:

1 The growth cycle of forage grass (we also need to consider whether it is less than 25 days, assuming that the cycle is 7 days and 35 days, there will be a big difference between the two cases 7 days, the grass that has been eaten will soon complete a growth cycle and will no longer grow; And for 35 days, all the grass that has been eaten will grow non-stop).

2 The growth efficiency of a unit of forage (i.e., how much grass will grow in a day).

3 Grazing strategies

Mathematical thinking, one is everything, everything is one.

1. Problem description.

The problem of cattle grazing mainly involves the interrelationship between the number of cows, the number of days cattle graze, the amount of original grass, and the rate of change of grass (growth rate or withering rate), and the main difficulty is that grass is changing.

The typical cow grazing problem is the number of heads of cattle and the number of days they have eaten grass in two cases, and the number of heads of cattle or the number of days they have eaten grass in the third case is found. In the process of solving, we should pay attention to grasp the invariant, the original amount of grass, the speed of change of grass is generally unchanged, usually first find the speed of change of grass, and then find the original amount of grassland, and then find the number of cows or the number of days of grazing.

2. Typical example questions.

The amount of grass, the rate of change of grass, the number of days the cow eats grass or the number of heads of the cow are known.

1. A piece of grass originally had 60 parts, and 2 parts grew every day, 1 cow ate 1 part of grass a day, and 8 cows ate it in a few days?

8 cows eat 8 servings of grass a day.

Grass decreases by 8 2 6 (portions) per day

The number of days that cattle eat grass is 60 6 10 (days).

2. A piece of grass originally has 60 parts of grass, and 2 parts grow every day, 1 cow eats 1 part of grass a day, and eats it in 5 days, how many cows do you need?

Grass decreases by 60 5 12 (servings) per day

12 cows need to eat 12 parts of grass, and 2 cows are sent to eat 2 parts of grass that grow every day.

The number of heads of cattle is 12 2 14 (portions).

Knowing the number of cows and the number of days that cattle have eaten grass, find the original amount of grass and the amount of grass change.

3. There is a meadow that can be eaten for 8 cows for 10 days and 4 cows for 18 days. Find the amount of original grass and the amount of change in grass.

Let's say 1 cow eats 1 serving of grass in 1 day.

8 10 80 (servings).

4 18 72 (servings).

After 8 days, 8 servings of grass are missing.

The rate of wilting of grass (80 72) (18 10) 1 (portion).

The original grass amount is 80 10 1 90 (parts).

The number of heads of cattle and the number of days that cattle eat grass are known for the two cases, and the number of heads of cattle or the number of days for cattle grazing in the third case is found.

4. If there is a pasture that can be eaten by 10 cows for 20 days and 15 cows for 10 days, how many days can it be eaten by 25 cows?

Suppose 1 cow eats 1 serving of grass a day, and the change rate of grass and the amount of original grass remain unchanged.

The growth rate of grass (10 20 15 10) (20 10) 5 (portions).

The original grass volume is 10 20 20 5 100 (copies).

Number of days 100 (25, 5) 5 (days).

5. If there is a pasture that can be eaten by 10 cows for 20 days and 15 cows for 10 days, how many cows can it eat for 5 days?

Suppose 1 cow eats 1 serving of grass a day, and the change rate of grass and the amount of original grass remain unchanged.

The growth rate of grass (10 20 15 10) (20 10) 5 (portions).

The original grass volume is 10 20 20 5 100 (copies).

Every day, 5 servings of grass are specially eaten by 5 cows.

Number of heads 100 5 5 25 (heads).

Elementary School Math Cow Eating Grass Problem Episode 1, How Many Cows Eat for 15 Days?

If you master a simple and fast solution to a certain knowledge point in the process of reviewing and preparing for the test, then it will definitely make our problem-solving efficiency achieve twice the result with half the effort. Today, I will share with you an efficient solution to the problem of "cows eating grass" in the quantitative relationship of "line test".

1. Model features.

Let's start with a general example: There is a patch of grass in the pasture, the grass grows at a uniform rate every day, and the grass can be eaten by 10 cows for 20 days, or 15 cows for 10 days, and how many days can it be eaten by 25 cows?

It is not difficult to see that the biggest feature on the outside is that the question stem and the question form an obvious proportional structure, which can be eaten by several cows for several days in a row; First, there is a certain amount of primitive grass in the pasture at the beginning of the pasture, and second, the grass itself grows at a uniform rate every day, which will increase the amount of forage (in some topics, the grass will wither at a uniform rate, which will reduce the amount of grass), and if the cattle are put to eat the grass, the amount of forage will be reduced, that is to say, there are two factors that affect the amount of forage at the same time. Summarizing the above analysis, the "cattle grazing" problem has the following characteristics:

1. Obvious proportional structure;

2. At the beginning of the pasture, there is a certain amount of pasture;

3. There are two factors in the follow-up process that affect the amount of forage at the same time.

Second, the model column.

We abstract the model and assume that the original grass grows evenly on a line segment (ab), that the new grass grows in a straight line from the end of the line segment (b), and that the cattle graze at a uniform rate from the end of the line segment (a). When the cow has eaten all the grass, it means that the cow has just finished eating the last new grass. In other words, the cow reaches the far right end of all the grass at the same time as the newborn grass (c).

For the amount of forage eaten by cattle, the amount of primitive forage, and the amount of new forage, there is a relationship as shown in the following figure:

For the problem type of uniform withering of pasture, we can abstract the model into an encounter model, just change the minus sign in the formula to the plus sign, and get: , call this model the encounter type cow grazing, and then we take the catch-up type cow eating grass as an example.

3. Model solving.

Back to the topic: There is a patch of grass in the pasture that grows at an even rate every day, and this grass can be eaten by 10 cows for 20 days, or 15 cows for 10 days, and asked for 25 cows for how many days?

Here are some of the advantages of this method: in the process of solving the problem, we eliminate the yuan y through the equation; Through the proportional method, the difference is made horizontally and the element x is eliminated, so that the time t of our final required solution is directly calculated, which achieves the purpose of convenience and efficiency. When you are proficient in using it, you can see the answer directly without even using a pen.

Establish. A cow.

Eat 1 serving of grass per day.

The grass produced by each shed and this pure chain (21*8-24*5) 3=16 is 16 cows.

The problem of cattle grazing, also known as the problem of growth and decline or Newton's pasture, was proposed by the great British scientist Newton in the 17th century. The condition of a typical cow grazing problem is to assume that the growth rate of grass is fixed, and the number of days it takes for different numbers of cattle to eat the same grassland are different, and how many days can be eaten by several cows eating this grassland. Because the number of days eaten is different, and the grass grows every day, the stock of grass constantly changes with the number of days the cow eats.

There are four basic formulas commonly used to solve the problem of cattle grazing, which are:

1) The growth rate of the grass, the corresponding number of cows, the number of days eaten more, the corresponding number of cowheads, the number of days eaten less (more days eaten, fewer days eaten);

2) The amount of original grass, the number of cattle heads, the number of days eaten, the growth rate of grass, the number of days eaten; `

3) the number of days eaten, the amount of original grass (the number of cows, the growth rate of grass);

4) The number of cattle heads, the amount of grass, the number of days eaten, and the growth rate of grass.

These four formulas are the basis for solving the problem of growth and decline.

Since the grass is constantly growing in the process of grazing the cows, the key to solving the problem of growth and decline is to find ways to find invariants from change. The original grass on the pasture is unchanged, and although the new grass is changing, the amount of new grass growing every day should be the same because it grows at a uniform rate. It is because of this invariant that the above four basic formulas can be derived.

The problem of cattle grazing is often given that different numbers of cattle eat the same grass, and the field has both the original grass and the new grass that grows every day. Due to the different number of cows that eat grass, find out how many days the grass in the field can be eaten by several cows.

The key to solving the problem is to figure out the known conditions, conduct comparative analysis, and then find the number of new grass growing every day, and then find the amount of original grass in the grassland, and then solve the problem that the question is always asked.

The basic quantitative relationship for this type of problem is:

1.(Number of cows, days of grazing more - number of cows, number of days of grazing) (number of days of eating more - days of eating less) = the amount of new grass growing in the grass per day.

2.Number of cows Grass days - new growth per day Number of grass days = original grass in the meadow.

You come to me directly.