In a long-distance race held in a county, the athletes run 3 kilometers away from the starting point to return to the starting point. The leading athlete runs 310 kilometers per minute, and the last athlete runs 290 meters per minute. How many minutes after the start do the two athletes meet? How many meters away from the starting point when they meet?

In a long-distance race held in a county, the athletes run 3 kilometers away from the starting point to return to the starting point. The leading athlete runs 310 kilometers per minute, and the last athlete runs 290 meters per minute. How many minutes after the start do the two athletes meet? How many meters away from the starting point when they meet?

Let's set the distance back to the point x meters, then it's the same according to the time they run when they meet
formulation of equation
（3000-x）÷290=（3000+x）÷310
The solution is x = 100
Time equals (3000-100) △ 290 = 10 (minutes)
To solve these problems, first of all, find out the equivalent relationship. For example, in this problem, the equivalent relationship is equal time
Then we use the unknown number x to represent the equivalent relation, and list the equation, which is a good solution

On a straight road, Xiao Ming and Xiao Gang ride bicycles from a and B, 400 meters apart. Xiao Ming travels 240 meters per minute and Xiao Gang 160 meters per minute. If they keep going at this speed, will they meet? If you don't think we will meet, please write down the reason; if you think we will meet, ask for a few minutes to meet?

(1) 400 (240 + 160) = 400 (240 + 160) = 400 (400) = 1 (min) answer: walk in opposite directions and meet in 1 minute. (2) 400 (240-160) = 400 (240-160) = 80 = 5 (min) answer: meet in 5 minutes

After two hours of meeting, they continued to move forward at the same speed. After another 1.5 hours, a arrived at B, and B was 35 km away from A. how many kilometers did they travel per hour?

It takes 2 + 1.5 = 3.5 hours for Party A to complete the whole journey, so Party A takes 1 / 3.5 = 2 / 7 of the whole journey per hour, Party B takes 1 / 2 of the whole journey per hour, so Party B takes 1 / 2-2 / 7 = 3 / 143.5 hours, Party B takes 3 / 14 * 3.5 = 3 / 4 of the whole journey, so the whole journey is 35 / (1-3 / 4) = 140 km, so Party A takes 140 × 2 / 7 = 40 km per hour

A mathematical reasoning problem: the five couples of Zhang, Wang, Li, Zhao and Chen get together. When they meet, they shake hands and greet each other. Mr. Wang asks everyone in private curiously
Zhang, Wang, Li, Zhao, Chen and their five couples get together. They shake hands to greet each other when they meet. Mr. Wang curiously asks everyone (including his wife) in private to inquire about the number of handshakes just now. The answer surprised him. No two of the nine people shake hands the same number. Mrs. Wang shakes hands () times,

This is an interesting problem of logical reasoning put forward by Martin Gardner, a famous contemporary master of popular science in mathematics. Tan Xiangbai, a Chinese writer of popular science in mathematics, introduced this interesting problem in his wide angle of Mathematics (Jiangsu Education Press, 1998), In addition, for various reasons, people who can shake hands may not always shake hands. Therefore, among them, the person who shakes hands the most should not shake hands more than 8 times. Mr. Wang has asked nine people to shake hands differently. Therefore, the number of times they shake hands should be 0, 1 and 2 respectively The analysis shows that the person who shakes hands for 8 times and the person who shakes hands for zero times must be a couple. This is because the person who shakes hands for 8 times, let's assume Mr. Zhang, he must shake hands with each of the four couples except Mrs. Zhang, If the number of handshakes is zero, it can only be Mrs. Zhang. In this way, the number of handshakes of Mr. and Mrs. Zhang has been determined and excluded. Since the total number of handshakes is 8, it must be a couple, and no two of the nine people shake hands the same number, so only Mr. Wang and Mrs. Wang shake hands four times
Reference materials: Mathematics for middle school students, No.21, 2003