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牛顿提出了一个非常有名的牛吃草问题,人们称它为牛顿问题：三头牛在两星期内能吃完两亩地上原有的草和两星期中生长的草；两头牛在四星期内能吃完两亩地上原有的草和四星期中生长的草,问要多少头牛才能在六星期内吃完六亩地上原有的草和六星期中生长的草？解：设要x头牛在六星期内吃完六亩地上原有的草和六星期中生长的草,设每亩地原有草a千克,每亩地每星期长草b千克,每头牛每星期吃草c千克,根据题意得方程组 2－1得4b=2c,c=2b.把c=2b代入1得a=4b.把a=4b,c=2b代入3得24b＋36=x·12b.∵b≠0,∴x=5.如果把这道题稍加演变,可变为形式新颖内容生动的应用题.这种题型常在竞赛中出现. 这些演变后的题目,虽然形式各异,但数量关系和解法却完全相同.现举例如下：例1 有一口深水井,有一股水以匀速向井内涌进,若用5人打水,需2小时打干；用7人打水,需1小时20分打干,假若每人打水能力相等,现在要1小时打干,问要多少人？解：设一小时打干要x人,设水井原有水量为a升,每小时涌进水量为b升,每人每小时打水量为c升,根据题意可得方程组：
Newton proposed a very famous cattle grazing problem. People called it the Newton problem: Three cows can eat two acres of grassland and two weeks of growing grass within two weeks; two cows within four weeks. After eating two acres of grass and four weeks of growing grass, how many heads of cattle can eat six acres of grass and six weeks of grass growing within six weeks? Solution: Set x cows to eat six acres of grassland and grass growing in six weeks within six weeks. Set a kilogram of original grass per acre, and b kilograms of grass per acre each week. Cattle grazing every week c kilograms, according to the meaning of the equation 2-1 get 4b = 2c, c = 2b. C = 2b into 1 to get a = 4b. A = 4b, c = 2b into 3 24b + 36 = x·12b.∵b≠0,∴x=5. If this question is slightly evolved, it can be used as a vivid application of novel content. Such questions often appear in competitions. These evolved questions, Although the forms are different, the quantitative relationship and solution are exactly the same. Here are some examples: Example 1 There is a deep well, and there is a constant flow of water into the well. If 5 people draw water, it takes 2 hours to dry. It takes 1 hour and 20 minutes for people to draw water. If the ability of each person to draw water is equal, it will take 1 hour to dry. How many people are asked? Solution: Set an hour to kill x, set the original amount of water in the well to be a litre, the amount of water pouring in per hour is b litres, and the amount of water drawn per person per hour is c litres. According to the question meaning, the equations can be obtained: