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现行初中教材代数第三册P157第20题:“A、B地间的距离为36里。甲从A地,乙从B地同时出发相向而行,二人相遇后,甲再走2小时30分到达B地,乙再走1小时36分到达A地。求二人的速度。”这是一类常见的“相遇问题”,解法很多。但所列的方程(组)解法较繁。本文先介绍“相遇问题”的一个性质,再说它在解这类问题时的应用。性质:甲、乙分别从A、B两地出发相向而行自出发到相遇所用时间的积,等于相遇后甲到达B处与乙到达A处所用时间的积。证明:设甲、乙分别从A、B出发相向而行,在C处相遇,甲行AC需时间x,乙行BC需
The current junior middle school textbook Algebra Volume III P157 Question 20: “The distance between A and B is 36 miles. A is from A and B is from B to the same place. After the two meet, A goes another 2 hours 30. After arriving at B, B walks again for 1 hour and 36 minutes to reach A. Find the speed of the two. “This is a common ”encounter problem.“ There are many solutions. However, the listed equations (groups) solution is more complicated. This article first introduces the nature of the ”encounter problem" and then its application in solving such problems. Nature: The product of the time taken by A and B from A and B to each other and the time from the start to the encounter are equal to the product of the time taken by A to reach B and B to reach A. Prove that: Set A and B to start from A and B respectively. When meeting at C, A-line AC needs time x, B-BC needs