Cow Eating Grass Formula? What is the formula for the cow grazing problem?

There is no formula for cows to eat herbs, but I summarized it a few years ago.

Let's say a cow eats 1 amount of grass in a day

The known time to find the number of heads: the amount of raw grass time to grow per day.

This is all at the general level of thinking, and the rest that may not be mentioned is relatively simple.

The cow grazing problem is a classic math problem that usually involves finding a state of equilibrium in the grass that allows the grass to continue to grow. This problem can be represented by the following formula:

1.The growth rate of the grass = (the corresponding number of cow heads eat more days - the corresponding number of cow heads eat less days) (the number of days that eat more - the number of days that eat less).

2.The amount of original grass = the number of cattle head the number of days eaten - the growth rate of the grass The number of days eaten.

3.Number of days eaten = amount of grass (number of cattle head - grass growth rate).

4.Number of cattle heads = original amount of grass Number of days eaten + growth rate of grass.

These formulas can help us understand the area of grass that can sustain the continuous growth of the grass when a certain number of cattle are placed on the grass.

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

1) The growth rate of grass = (the corresponding number of cow heads, the number of days that eat more, the corresponding number of cow heads, the number of days that eat less) (the number of days that eat more, the number of days that eat less);

2) The amount of original grass = the number of cattle head The number of days eaten The growth rate of the grass The number of days eaten;

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

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

These four formulas are the basis for solving Newton's problems. Since the grass is constantly growing in the process of grazing in the process of cattle grazing, 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.

Additive operations. In the formula with parentheses, it is necessary to calculate the inside of (small parentheses) first, then the inside (middle brackets), and finally the outside of the parentheses.

1. Four mixed operation sequences: when the same level is calculated, it is calculated from left to right; In two-level operations, multiplication and division are calculated first, and addition and subtraction are calculated later.

When there are parentheses, count the inside of the brackets first, and then the outside of the brackets; When there are multiple layers of parentheses, count the ones in the small brackets first, then the inside of the middle brackets, then the inside of the braces, and finally the outside of the brackets.

2. Multiplication is a simple operation of addition, and division is a simple operation of subtraction. Subtraction and addition are inverses of each other, and division and multiplication are inverses of each other.

Several additions are added together, and the position of the addition can be arbitrarily exchanged; Or add a few additions and then add them to the other additions, and their sum does not change.

(1) The speed at which grass grows per day = (number of cows, more days - number of cows, fewer days) (more days - fewer days).

2) Original grass = number of cow heads Number of days eaten - speed of growing grass per day Number of days eaten (3) Number of days eaten = original grass (number of cow heads - speed of growing grass per day) Number of cow heads = number of days of original grass eaten + speed of growing grass per day.

The formula for the cow grazing problem is:1) The growth rate of grass = (the corresponding number of cow heads, the number of days that eat more, the corresponding number of cow heads, the number of days that eat less) (the number of days that eat more, the number of days that eat less);

2) The amount of original grass = the number of cattle head The number of days eaten The growth rate of the grass The number of days eaten;

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

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

For example, a station starts queuing a few minutes before the ticket is checked, and the number of passengers comes every minute is the same. From the start of the ticket gate to the disappearance of the queue for the ticket gate, it takes 30 minutes to open 4 ticket gates at the same time and 20 minutes to open 5 ticket gates at the same time. How many minutes does it take to open 7 wickets at the same time?

With this kind of theme, the ticket gate can be regarded as a cow and the passenger as a grass. Direct set of formulas - passenger speed per minute = (4 30-5 20) (30-20) = 2.

Passengers in line = (5-2) 20=60.

60=（7-2）t。

t=12。

U Ruri Dudy is the fourth brother of **Kakashi Express.

1) The growth rate of the grass = (the corresponding number of cow heads eat more days the corresponding number of cow heads eat less days) (the number of days that eat more and eat less days);

2) The amount of original grass = the number of cattle head The number of days eaten The growth rate of the grass The number of days eaten;

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

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

The formula for the cow grazing problem is:

1. (The amount of grass eaten by all cattle per day and the amount of new grass growing in the grass per day) Number of days The initial amount of grass.

2. The amount of new grass growing in the grassland every day (more days x corresponding to the number of cattle heads, less days x corresponding to the number of cattle heads).

More days—fewer days).

3. The number of days the cow eats grass The initial amount of grass (the amount of grass that the cow eats every day, the amount of grass that grows new every day).

Example of a cow grazing problem.

A piece of grass that grows at a uniform rate can feed 16 cows for 20 days or 100 sheep for 12 days. If the amount of grass eaten by a cow in a day is equal to the amount of grass eaten by 5 sheep in a day, how many days can this grass be eaten by 10 cows and 75 sheep together?

Earlier in the question, we talked about cattle and sheep, two different animals, different numbers, different days. So we need to convert it to the same animal so that we can do the calculations. At the end of the question, it is said that the amount of grass eaten by 1 cow in one day is equal to the amount of grass eaten by 5 sheep in one day.

This is a very important piece of information. The amount of grass eaten by 100 sheep per day is actually equivalent to the consumption of grass for 100 5=20 cows.

Let's take the amount of grass eaten by each cow in a day as 1 serving, and assume that the amount of grass recovered per day is x, then we can make an equation.

According to this equation, we can calculate this x=10, which means that the amount of grass to recover 10 portions per day.

According to the theme, the original amount of grass in the grassland is. (16 20) (20 10) 320-200 = 120 (parts).

The amount of grass eaten by 10 cows and 75 sheep per day is actually equivalent to: 10 + 75 5 = 25 (head) of cattle eat grass.

Pure amount of grass consumed per day: 25-10=15 (servings).

120 (25-10) 120 15=8 (days).

A: This meadow can feed 10 cows and 75 sheep for 8 days.

The amount of grass eaten by the cow - the amount of grass grown = the amount of grass consumed.

There are four basic formulas commonly used to solve the problem of cattle eating grass, which are 1) the growth rate of grass = (the corresponding number of cow heads eat more days the corresponding number of cow heads eat less days) (the number of days eaten more days eat less days);

2) The amount of original grass = the number of cattle head The number of days eaten The growth rate of the grass The number of days eaten; 3) The number of days eaten = the amount of grass (the number of cows, the growth rate of grass);

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

These four formulas are the basis for solving Newton's problems.

The amount of grass eaten by the cow - the amount of grass grown = the amount of grass consumed.

There are four basic formulas commonly used to solve the problem of cattle eating grass, which are 1) the growth rate of grass = (the corresponding number of cow heads eat more days the corresponding number of cow heads eat less days) (the number of days eaten more days eat less days);

2) The amount of original grass = the number of cattle head The number of days eaten The growth rate of the grass The number of days eaten; 3) The number of days eaten = the amount of grass (the number of cows, the growth rate of grass);

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

These four formulas are the basis for solving Newton's problems.

The formula for the problem of cow grazing in the relationship between the number of lines and the test:

Catch-up formula: original grass = (grass eaten by cattle per day - grass grown per day) * number of days.

Encounter formula: original grass = (grass eaten by cattle per day + amount of grass reduced per day for other reasons) * number of days.

Extremum formula: Use the original amount of grass = (the amount of grass eaten by cattle per day - the grass grown per day) days to find the growth rate of grass, and the number of heads of the largest cow = x.

Multiple pasture cattle grazing problems.

Formula: Find the "least common multiple" of the area of multiple pastures by the least common multiple, and then convert all the areas into the "least common multiple" and change the number of cattle heads accordingly, which is transformed into the original standard cattle grazing problem with the same amount of grass.

Standard cattle grazing problem.

Generally, the amount of grass eaten by each cow per day is set as the unit of 1, the growth rate of grass is x, the number of heads of cattle is n, and the number of days is t. That is, the original grass = (n-x)*t