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Classical problems of Olympic mathematics in the sixth grade of primary school and the second encounter
Tips for pursuing knowledge points;

A and b walk at the same time One walks fast, the other walks slowly. When you walk slowly in front, you can catch up quickly in a while. This has created a "catch-up problem." In essence, it is necessary to calculate the distance that fast walkers walk more than slow walkers in a certain period of time, that is, to calculate the speed difference between them. If a walks fast and b walks slowly, in the same time (catch-up time):

Catch-up distance = distance a walks-distance b walks.

= speed of A × catch-up time-speed of B × catch-up time

= speed difference × catch-up time

The core is the problem of "speed difference".

Knowledge tips for the second meeting:

A starts from place A, B starts from place B, and meets at place C. After meeting, A continues to go to place B and then returns, and B continues to go to place A and then returns, and meets again at place D. Generally, we know the distance between AC and AD, mainly grasping that the distance at the second meeting is twice that at the first meeting.

1. An express train 170 meters, traveling at a speed of 23 meters per second, and a slow train 130 meters, traveling at a speed of 18 meters per second. The express train catches up with the local train from behind, and it takes several seconds to overtake the local train.

2. The distance between A and B is 100 km, and both A car and tractor travel from A to B. When the car starts, the tractor has already started15km; When the car arrived at B, the tractor was 0/0 kilometers away from B/KLOC ... So how many kilometers away from B did the car catch up with the tractor?

3. The circumference of the circular runway is 500m. Party A and Party B set off clockwise along the circular runway at the same time and place. Party A runs 50 meters per minute and Party B runs 40 meters per minute. They should stop to rest every 200 meters 1 minute. How many minutes does it take for Party A to catch up with Party B for the first time?

4.A and B are driving in opposite directions at the same time, meet at a distance of 54 kilometers from B, return immediately after arriving at the other station, and meet at a distance of 42 kilometers from A ... Excuse me, how many kilometers is there between A and B?

Two cars were driving in opposite directions from A and B at the same time, and they met 52 kilometers away from A city. After arriving in the other city, they immediately returned along the original road at the original speed and met at a distance of 44 kilometers from a city. The two cities are thousands of meters apart.

6. Two cars, A and B, leave from A and bilibili relatively simultaneously. The first meeting was 90 kilometers away from Station A, and then they continued to drive at the original speed, and immediately returned along the original road after arriving at each other's starting station. The distance from station A at the second meeting accounts for 65% of the total length of the two stations in AB. Find the distance between two stations in AB.