Current location - Training Enrollment Network - Mathematics courses - Mathematical problems of seventh grade on circular runway
Mathematical problems of seventh grade on circular runway
1. 18, A caught up with B and began to overtake B. At 23: 00, A caught up with B again. Caption: A ran 400 meters more than B in 5 minutes. So the speed difference between Party A and Party B is 400 ÷ 5 = 80m.

2. 15, Party A speeds up. 18, Party A catches up with Party B and begins to overtake. Description: Party A caught up with Party B in 3 minutes, but the difference between them was 80×3=240 (meters), which was caused by Party B being faster than Party A in the first 15 minutes. So it turns out that Party B is faster than Party A..

3. Let the original speed of A be x meters per minute, and now the speed of A is x+96 meters per minute.

15x+(x+96)×(23 5/6- 15)= 10000。

x=384

So the original B speed: 384+ 16=400 meters.

B The time to finish the race is: 10000÷400=25 minutes.

In the whole process, B moves at a uniform speed; Before 15 minutes, A is slow, after 15 minutes, A accelerates until the end.

In the first18th minute, A caught up with B and began to overtake B. In the 23rd minute, A caught up with B again.

It can be seen that after acceleration, A makes one more trip than B in 23- 18=5 minutes, that is, 400 meters, so A makes 400÷5=80 meters more trips per minute than B.

At the 23rd minute and 50s, A reaches the finish line, and the distance from B to the finish line should still be 80m/min×(23 minutes and 50s- 18 minutes) 1400/3m.

So the speed of B is (10000-1400/3) m/(23 minutes and 50 seconds) =400 m/min.

So the time for B to finish the race is 10000/400=25 minutes.