Problem description:
Suppose there is a 10-kilometer-long runway, and two athletes start from the same starting point at the same time. One athlete has a speed of 15 kilometers per hour and the other athlete has a speed of 20 kilometers per hour. So when and where did the two athletes meet?
Problem solving process:
First of all, you need to know that the condition for two athletes to meet is that they run the same distance and have the same time. Therefore, we can solve it by setting variables and listing equations.
Suppose one of the athletes runs for x hours, then the distance he runs is 15x kilometers; The other runner ran 20(x-0.5) kilometers, because he was faster than the first runner, so he ran 0.5 hours less. Because they run the same distance, the following equation can be obtained:
15x=20(x?0.5)
After simplification, you can get:
Therefore, the two athletes will meet in two hours. The location where they met can be obtained by substituting the formula:
15x=30
Therefore, the two athletes will meet 6 kilometers before the 10-kilometer finish line.
Analysis:
This problem needs to be applied to basic kinematics knowledge, such as the relationship between speed, time and distance. By setting variables, listing equations and solving them, the answer to the question can be obtained.
In addition, this problem can also be solved from a more intuitive perspective. The distance difference between the two athletes is 5 kilometers per hour, that is, the first athlete can only walk 5 kilometers per hour. Because they started in the same position, when the second athlete caught up with the first athlete, the first athlete actually only walked half of the 10 kilometers, that is, 5 kilometers. Therefore, the two athletes will meet at the sixth kilometer, half of the 10 kilometers before the finish line.
In a word, although this problem looks simple, it contains profound physical significance and practical application.
