11. How much does the rest cost if found directly?
A: (1-2/5)*(1-2/3)*(1-2/5)a< /p>
B: (1-2/3)*(1-2/5)*(1-2/3)b
A:B=2:1:a:b =9:5
12. If we want the trams to pass each other every 4 minutes, we can find out by drawing a continuation diagram:
Both places must start at the same time and 8 minutes apart
p>
Suppose the entire trip is 1, then:
We can know that the speed of the tram is 1/56, then the distance between the two oncoming trams is 1 /7
At this time, Xiao Zhang crosses every 5 minutes Towards an oncoming tram
That is to say: 1/7 of the distance is covered by the tram and Xiao Zhang in 5 minutes. Then, Xiao Zhang's speed can be calculated: (1/7)/5 -1/56=3/280
Similarly: Xiao Wang encounters an oncoming tram every 6 minutes< /p. >
Then Xiao Wang's speed: (1/7) /6-1/56=1/168
Then whend Xiao Zhang and Xiao Wang meet on the way, the time they walked is
1/(3/280+1/ 168)=840/14=60 points
I think I'm not the first to explain this idea and question here
But I hope the poster can see it clearly
Consider it appropriate
p>I hope to adopt it
I hope it can help you
Classic Mathematical Olympiad Questions for Primary School Students: Shift Problem at multiple people
On the same distance Inside, it takes 6 minutes for the two trams to travel relative to each other, 8 minutes for the tram to travel relative to Mingming, and 9 minutes for the tram and Lingling to move relative to each other.
Let this distance be equal to s, the speed of the tram is d, and the speed of Mingming is m, the speed of Lingling is L
Then
s/(d+d)=6 ①
s/(d+m)=8 ②< /p>
s/(d+l) = 9 ③
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 met. The time is 12/5 times that of the entire tram journey< /p>
=45*12/5 = 108 minutes.
Multi-person route problem for the Mathematics Olympiad
Multi-person route-- -This type of problem mainly involves 3 people. The main problem to study is to find the moment when the first two people meet or catch up, and the position of the third person. combine the three people The problem turns into finding a 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 lefthey in 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 3 minutes later. What is the perimeter of this flower garden?
2. A, B and C walk at 60 meters per minute, B walks at 50 meters per minute and C. walks 50 meters per minute. Walk 40 meters. 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 first and travels at 27 kilometers per hour. rode at a speed of 34 kilometers per hour for 34 minutes, then athlete B rode at a speed of 36 kilometers per hour for 25 minutes, then athlete C rode 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, and each of them sends a tram there at a certain time. is a tram. Xiao Zhang and Xiao Wang ride bicycles from locations A and B respectively, each tram meets an oncoming tram every 4 minutes; Wang encounters an oncoming tram every 6 minutes. It is known that the tram runs for 56 minutes, so when Xiao Zhang and Xiao Wang meet on the way, they have walked for 5 minutes.
5. A, B and C go from East Village to West Village at the same time. A cycles 12 kilometers per hour faster than B and 15 kilometers per hour than C. A rides 3.5 hours to reach West Village. and returns immediately. Meet B 30 kilometers from Xicun and ask: How long did it take C to meet A?
6. There are three people, A, B and C, and A comes from the east of the Village, B and B left from the West Village at the same time and headed towards the other. On the way, A and B met C 6 minutes later. We know that A walks 100 meters per minute, B walks 80 meters per minute and C walks 75 meters per minute. How many meters are there between the east and west villages?
7. The walking speeds of A, B and C are 30 meters, 40 meters respectively and 50 meters per minute. 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. There are three people A, B and C. The people 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. 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 later. Question: How many meters is the perimeter of this flower garden?
9. AB is 30 kilometers apart. at the same time and must arrive at the same time. There are now two bikes, but no one is allowed to take them with them, but the bikes can be dropped off somewhere halfway and the people behind 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 left the same place at the same time and walked in a flower garden. Two people, B and C, were walking in the same direction and A, B and C were walking opposite each other. A walks 40 meters per minute, B walks 38 meters per minute and C walks 36 meterss per minute. On the way, A and B met C 3 minutes later. 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 hour, 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 arrived by behind A dog runsrear, and when it reaches bridge B, the train has just arrived at B; the other dog runs forward, and when it reaches bridge A, the train also reaches A. The speed of the two puppies is 6 meters per person. Second, ask how fast is the train?
13. Xiao Ming walked along the escalator going up and down. He has broken through level 150. His classmate Xiao Gang. Walking along the escalator from bottom to top, there are 75 steps. If Xiao Ming's walking speed is 3 times that of Xiao Gang, how many steps of the escalator can be seen?
p>
14. A car driving from point A to point B can arrive one hour earlier than the original time if the speed is increased by 20% if it travels 120 kilometers at the original speed, the original speed can be increased again by 25%; %, you can arrive 40 minutes earlier. How many kilometers are therebetween places A and B?
15. A dog chases a rabbit and the time it takes the dog to get there. jumping 6 times is The rabbit can only jump 5 times. The distance for the dog to jump 4 times is the same as the distance for the rabbit to jump 7 times. After the rabbit ran 5.5 kilometers, the dog started chasing it. How far did the rabbit travel before the dog caught up with him.
16. In a race between three animals, the speed of the fox is 4/5 of that of the rabbit, and the speed of the rabbit is twice that of the squirrel . The squirrel runs 12 meters less in a minute than the fox. Question: How many meters further does the rabbit run than the fox in half a minute?
17.A and B. travel respectively at speeds of 160 kilometers per hour and 20 kilometers per hour, and their length is 210 kilometers. Starting at the same time, same place and in the same direction on the journeyheretic. 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 speeds of the two cars are exactly equal, what are their speeds? How many kilometers have they traveled respectively?
18. Locations A and B are separated by 125 kilometers. Two people, A and B, leave from places A and B at the same time. time on the bike. Walk towards 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 arrives at 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? /p>