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小学数学牛吃草问题(Primary school mathematics cattle grazing problem)
小学数学牛吃草问题(Primary school mathematics cattle grazing problem)
Primary school mathematics cattle grazing problem
A grassy pastures, cattle grazing grass and continuous uniform growth, 27 cows, 6 days can eat all the pasture grass; it will take 9 days to finish all 23 cattle pasture grass, if 21 cows to eat, eat a few days?
The question is called: Newton problem, complete solution to the problem: assume that every cows daily grazing amount is 1, then the first 6 days of grazing amount is 27 * 6=162; 23 cows, 9 days of grazing amount is 23 * 9=207; 27. The difference is 207 and 162 (9-6) to grow new grass, so the amount of grass pasture every day a new growth is (207-162) / (9-6) =15 for 6 days 27 cattle grazing amount was 162, the 6 day of the new long grass and 15 * 6=90, so that the original plan of pasture 162-90=72 day long enough pasture grass 15 cows eat for a day, every day for 21 cows in 15 cows eat new long grass, the rest of the 21-15=6 (head) eat the original grass. So the pasture grass can eat 72 / 6=12 (days), which is also the pasture grass enough 21 cows eat for 12 days.
General formula: [27 (23 x 6- x 9-27 x 6) / (9-6) * 6] / [21- (9-27 * 23 * 6) / (9-6)]=12 (days)
The problem of cattle grazing is a kind of difficult problem of primary school Olympiad. I remember seeing in a Book: the problem of cattle grazing is chasing and problems, and the problem of cattle grazing is the engineering problem.. For the first half of the sentence is well understood, when the children speak, but also by chasing and thinking of the problem in terms of. But for the second half, I didnt figure it out until last week.
Last week, the lesson is to give a class about Ren Hua School Textbooks in this class is the sixth grade, I have been brought up from the second grade, learned from one year to six of the whole Ren Hua school textbooks, adhere to the student is not much, but each is very strong, the learning effect is very obvious, too see why this set of textbooks enduring.
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