Multi-person Route Math Olympiad Problem
Multi-person Route --- This type of problem mainly involves 3 people. The main problem is to find the time when the first two people meet or meet again. up, and the third person Personal position, the idea of solving the problem is to transform the three-way problem by finding the relationship between two people. Below are the classic question types of multi-person directions questions compiled by me on Boutique Learning Network for your reference.
1. Three people, A, B and C, left the same place at the same time and walked through a flower garden. B and C walked in the same direction, and A moved away from B. and C. A is 40 meters per minute, B is 38 meters per minute, and C is 36 meters per minute. After departure, A and B met and then met C 3minutes later. What is the perimeter of this flower garden?
2. A, B and C walk at 60 meters per minute, B walk at 50 meters per minute and C walk at 40 meters per minute. Apart from A, and B and C start from B and move towards each other. After A and B meet, they meet C again 15 minutes later.
3. There are three cyclists. They play a relay game from city A to city B. Athlete A starts from city A and rides for 34 minutes at a speed of 27 kilometers per hour. at a speed of 36 kilometers per hour for 25 minutes, then athlete C drove at a speed of 30 kilometers per hour for 28 minutes to reach city B. What is the distance between cities A and B?
4. A and B are the departure stations of the trams. At a certain time, a tram leaves from both places at the same time. the bikes of A and B respectively, heading towards each other. Each tram meets a tram comingn reverse direction every 4 minutes; Xiao Zhang encounters an oncoming tram every 5 minutes; . It is known that the tram takes 56 minutes, so when Xiao Zhang and Xiao Wang meet on the way, they have walked for a few minutes.
5. A and B C and three people leave from East Village. in the West Village at the same time. A rode his bike 12 kilometers per hour faster than B and 15 kilometers per hour than C. A travels 3.5 hours to the West Village and returns immediately. Meet B 30 miles from West Village. Ask: How long did it take C to meet A?
6. There are three people, A, B, and C. A is from the East Village. , and B and C came from the West Village at the same time. They left and headed towards each other. On the way, A and B met 6 minutes later, and then met C again. We know that A walks 100 meters per minute, B walks 80 meters per minute and C walks 75 meters per minute. How muchhow many meters are there between the east and west villages?
7. The walking speeds of A, B and C are 30 meters, 40 meters and 50 meters per minute respectively. A and B are both in place A and C is in place B. A, B and C walk towards each other at the same time. C meets A 10 minutes after meeting B. How many meters are there between AB?
8. A, B and C start from the same point. stand at the same time and go around. While walking in a flower garden, two people, B and C, walk in the same direction, and A, B and C walk opposite each other. A walks 40 meters per minute, B walks 38 meters per minute and C walks 36 meters per minute. On the way, A and B met C 3 minutes after meeting. Question: And this flower garden? How many meters is the circumference?
9. AB is 30 kilometers from each other. A, B and C travel from A to B at the same time and must arrive at the same time. . There are now two bikes, but no oneis only allowed to take them, but the bikes can be left somewhere in the middle and the people who come after can take over. We know that the average speed of cycling is 20 kilometers per hour, the walking speed of A is 5 kilometers per hour and that of B and C is 4 kilometers per hour. How many hours does it take for three people to arrive at the same time. time?
10. Three people A, B and C leave the same place at the same time and walk in a flower garden. Two people, B and C, are walking in the same direction. B and C face each other. A walks 40 meters per minute, B walks 38 meters per minute and C walks 36 meters per minute. On the way, A and B met C 3 minutes after meeting. Question: What is the perimeter of this flower garden in meters?
11. There is a road from city A to city B, which is divided into three sections. On the first segment, the speed of the car is 40 kilometers per hourre, on the second segment the speed of the car is 90 kilometers per hour and on the third segment the speed of the car is 50 kilometers per hour. We know that the length of the first section of road is exactly twice that of the third section. Two cars leave from cities A and B at the same time and head towards each other. After 1 hour and 20 minutes, they meet 1/3 of the second section (1/3 from the direction from A to B). Question: How many kilometers separate A and B?
12. When the two puppies had just covered 1/3 of the length of the iron bridge, a train came from behind and a dog ran to let's go back. it reaches bridge B, the train just reaches B; the other dog runs forward, and when he reaches bridge A, the train also reaches A. The speed of both puppies is 6 meters per second. What is the speed of the train? ?
13. Xiao Ming walked along the escalator rising highdown. He took 150 steps. Classmate Xiaogang walked along the escalator from bottom to top and took 75 steps. if Xiao Ming's walking speed is 3 times that of Xiao Gang, what is the number of steps of the visible automatic ladder?
14. A car drives from point A to point B. If the speed the car is If you increase the original speed by 20%, you can arrive one hour earlier than the original time; if you drive 120 kilometers at the original speed and then increase the original speed by 25%, you can arrive 40 minutes earlier; are there several kilometers between A and B?
15. A dog chases a rabbit during the time it takes the dog to jump 6 times, the rabbit can only jump 5 times distance the dog jumps. times is the same as the distance the rabbit jumped 7 times. The rabbit ran 5.5 kilometers. After that the dog began to chase him, and the dogHe ran no matter how far he got before the dog caught up with him.
16. Three animals are running. The fox's speed is 4/5 that of the rabbit, and the rabbit's speed is twice that of the squirrel. The squirrel runs 12 meters shorter than the fox. a minute. Question: In half a minute, the rabbit runs faster than the fox. How many extra meters do you have to run?
17. A and B leave at the same time, in the same place, and in the same direction on a ring road 210 kilometers long, at respective speeds of 160 kilometers per hour and 20 kilometers per hour. Every time car A catches up to car B, car A slows down by a third and car B speeds up by a third. Question: When the speed of the two cars is exactly equal, what does it do?How many kilometers have they traveled respectively?
18. Locations A and B are 125 kilometers apart. Two people, A and B, respectively leave froms places A and B by bike at the same time, in the direction. each other. C rides a motorcycle at 63 kilometers per hour. Departing from A at the same time as A, shuttle between A and B (immediate return to the rendezvous with B, immediate return to the rendezvous with A), if the speed of A is 9 kilometers per hour, and when C comes to A for the second time (A, The time C left at the same time was the 0th time C returned to A). and B were 45 kilometers apart. Question: When C returned to A for the fourth time, how many meters were A and B separated. ?
Example 5 Locations A and B are the tram departure stations. A tram is sent from both places at the same time. Xiao Zhang and Xiao Wang cycle from locations A and B respectively.
on the same section Over the distance, it takes 6 minutes for the two trams to move relative to each other, 8 minutes for the tram to move relative to Mingming and 9 minutes for the tramr move relative to Lingling.
Let this distance s, the speed of the tram be d, Mingming The speed is m, and the speed of Lingling is L
Then
s/ (d+d)=6 ①
s/(d+m)=8 ②
s/(d+l) = 9 ③< /p>
① /② Get m/d = 1/4
①/③ Get l/d = 1/6
Therefore, the combined speed of Lingling and Mingming is
1/4+1/6=5/12
So the two people The meeting time is 12/5 times that of the entire tram ride
p>
=45*12/ 5 = 108 minutes.
Mathematics Olympiad Problem (Part 6) Masters, please help us~~
< p>The sum of the speed of two trams is 1/4, the speed of each tram is 1/8, the sum of the speeds of Xiao Zhang and the tram is 1/5, and the speed of Xiao Zhang is 1/5-1/8 = 3 /40The sum of the speeds of Xiao Wang and the tram are 1/6, the speed of Xiao Wang is 1/6-1/ 8 = 1/24 and the total distance is 56 × 1/8 = 7, so smallte When Zhang and Xiao Wang met on the way, they had already walked: 7÷(3/40+1/24)=60 minutes
11 How much is the rest if asked directly?< /p>
A.: (1-2/5)*(1-2/3)*(1-2/5)a
B: (1-2/3)* (1-2/5)* (1-2/3)b
A:B=2:1 gets:a:b=9:5
12. Make the tram reach us every 4 minutes By drawing. From the chase diagram you can know:
Both places should start 8 minutes apart at the same time
Suppose the whole journey takes 1, then:
You can know that the speed of the tram is 1/56. Then, the distance between two oncoming trams is 1/7.
At that time, Xiao Zhang encountered an oncoming tram every 5 minutes
It' i.e.: 1/7 of the distance was covered by the tram and Xiao Zhang in 5 minutes. After that, we can calculate Xiao Zhang's speed: (1/7)/5-1/56=3/280
Similarly: Xiao Wang renagainst an oncoming tram every 6 minutes
Then, the speed of Xiao Wang: (1/7)/6-1/56=1/168
Then the time that Xiao Zhang and Xiao Wang have been walking when they meet on the path is
1/(3/280+1/168)=840/14=60 points
I think I'm not the first to interpret this idea and question here
But I hope the poster understands it clearly
Consider it appropriate
I hope to adopt it
I hope this can help you