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同学们对环形问题感到棘手,下面以1996年天津市南开区一道中考模拟题为例,介绍环形问题的几种解法。 题目 甲乙两人沿环城公路跑步,甲跑完一周需3小时,现两人同时同地出发,相背而行相遇后,乙再跑2(2/7)小时才回到原出发点,求乙绕城跑一周需要多少小时? 解法一 设乙绕城跑一周用x小时,则甲每小时跑全程的1/3,每小时跑全程的1/x,甲、乙每小时共跑1/3+1/x,甲、乙同时出发,背向而行相遇时甲用的时间为1/(1/3+1/x),由题意得,
The classmates were intractable about the circular problem. In the following, an example of a simulated test in the middle school entrance examination in Nankai District, Tianjin City in 1996 was used as an example to introduce several solutions to the ring problem. The subjects A and B run along the ring road. It takes 3 hours to finish one round of the first round. The two are starting from the same place at the same time. After meeting each other, B goes back 2 (2/7) hours before returning to the original starting point. How many hours does B need to run around the city for a week? Solution A sets up B to run around the city for one week and uses X hours. Then A runs 1/3 of the hour, runs 1/x every hour, and A and B run 1 per hour. When 3+1/x, A and B start at the same time, the time spent facing back and facing each other is 1/(1/3+1/x).