The problem of cattle grazing, also known as wave problem or Newton problem, was put forward by British scientist Newton in17th century. The condition of typical cattle grazing problem is that the growth rate of grass is fixed, and the number of days for different cattle to eat the same grassland is different. How many cows can eat in this grassland for a few days? Because the eating days are different, the grass grows every day, and the stock of grass changes with the eating days of cattle.

Second, solve the problem of cattle grazing.

Four basic formulas are usually used to solve the problem of cattle grazing, namely:

(1) Find the growth rate of grass = (corresponding number of cattle × days of eating more-corresponding number of cattle × days of eating less) ÷ (days of eating more-days of eating less);

(2) Find the amount of raw grass = the number of cow heads × the number of eating days-the growth rate of grass × the number of eating days;

(3) the number of days to eat = the original amount of grass ÷ (the number of cattle-the growth rate of grass);

(4) Find the number of ox heads = the original amount of grass, the number of days to eat+the growth rate of grass.

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

Because the grass grows constantly when cattle eat grass, the key to solve the problem of growth and decline is to find invariants from changes. The original grass on the pasture has not changed. Although the new grass is changing, it is growing at a constant speed, so the daily growth of new grass should be constant. It is precisely because of this invariant that the above four basic formulas can be derived.

When cows eat grass, they often give different cows the same piece of grass. This land has both original grass and new grass that grows every day. Because the number of cows eating grass is different, how many cows can eat grass in this land for a few days?

For example; A meadow grows at a constant rate every week. This grassland can feed 12 cows for 9 weeks, or *** 15 cows for 6 weeks. So, how many weeks can this grassland feed nine cows?

12× 9 weeks = original grass +9 weeks new grass 15× 6 weeks = original grass +6 weeks new grass.

12× 9 weeks = original grass +9 weeks new grass 15× 6 weeks = original grass +6 weeks new grass.

Grassland has grass: 15×6-6×6=54.

Six cows eat new grass, and the other three cows eat original grass, 9-6=3 (head) 54÷3= 18 (day).

The key to solve the problem is to find out the known conditions and make a comparative analysis, so as to find out the number of new grass growing every day, and then find out the original number of grass in the grassland, and then answer the questions raised by general questions.

The basic quantitative relationship of this kind of problem is:

1. Eating days = original grass amount ÷ (number of ox heads-growth speed of grass)

2. Number of cattle × grazing days-new growth per day × grazing days = grassland grass.