The circular runway problem is one of the special field travel problems. It is a process in which many people (usually at least two people) meet or chase each other many times. To solve the problem that many people meet and chase each other many times, the key is to see whether we can accurately make a correct and reasonable line drawing for each trip described in the topic.

Second, after making a line chart, use it repeatedly:

Distance sum = meeting time × speed sum

Distance difference = chasing time × speed difference

Three, the general method to solve the problem of circular runway:

The problem of circular runway starts from the same place, and if the two directions are opposite, it will be encountered once every lap; If they travel in the same direction, they will meet each other every time they catch up. This equal relationship often becomes the key to solving our problems.

Four. Examples and answers of circular runway

Example 1. Party A and Party B set off at the same time with their backs to point A on the 400-meter circular runway. Eight minutes later, they met for the fifth time. It is known that Party A walks 0. 1 meter more than Party B every second. What is the shortest distance from the place where they met for the fifth time to point A along the runway?

Suppose the speed of B is x m/min0.1m/s = 6m/min8x+8x+8× 6 = 400× 5x =122122× 8 ÷ 400 = 2 ...1.

Example 2. The two men marched at a constant speed along the circular runway with a circumference of 400 meters. A ran for 4 minutes, B ran for 7 minutes, and started at the same place and in the same direction. A walked 65,438+00 laps and started in the opposite direction. Every time A catches up with B or meets head-on, they have to high-five. /kloc-how long did A walk and B walk during the high five?

Answer A walked 10 lap,10 * 400 = 4000m. Every time they high-five, A walks once (you can understand by drawing a picture), and then15 * 400 = 6000m * * walks 6000+4000 = 1000.

Example 3. Lin Ranran was once on a 450-meter-long circular runway. It is known that he runs 5 meters per second in the first half and 4 meters per second in the second half. How many seconds did he run in the second half?

The total solution time is 450÷(5+4)=50 seconds; The second half time =(225-4×50)÷5+50=55 seconds.