1, Xiao Ming, Xiao Feng and Xiao Guang all go from place A to place B. At 6 o'clock in the morning, Xiao Ming and Xiao Feng start from place A, Xiao Ming walks 5 kilometers per hour, Xiao Feng walks 4 kilometers per hour, Xiao Guang starts from place A at 8 o'clock in the morning, and Xiao Guang and Xiao Ming arrive at place B at 6 o'clock in the evening. When can Xiaoguang catch up with Xiaofeng?

Solution: Xiaoming walks 5 kilometers every hour and arrives at B from 6 am to 6 pm.

Distance between Party A and Party B: 5km * 12 = 60km,

Xiaoguang started from a place at 8 am and arrived at 6 pm.

Xiaoguang walks every hour: 60km/10 = 6km.

When did Xiaoguang catch up with Xiaofeng's pursuit? Xiaofeng walks 4 kilometers per hour. Xiaoguang walks 6 kilometers per hour.

4*2/(6-4)=4 hours, and Xiaoguang leaves from Party A at 8 am. 8+4= 12,

Xiaoguang caught up with Xiaofeng at noon 12.

2. Party A and Party B compete on a 400-meter circular runway. It is known that the average speed of Party B is 80 meters per minute, and the speed of Party A is 1.25 times that of Party B. Party A is ahead of Party B 100 meters. How many minutes does Party A lag behind before catching up with Party B?

Solution: (400 m-100m)/(1.25 * 80-80) =15min.

A: 15 minutes later, A can catch up with B.

A group of cyclists rode from A to B at a speed of 24 kilometers per hour. Two hours later, a motorcycle also rode from A to B at a speed of 56 kilometers per hour, and caught up with the cyclist at half the distance from A to B. Q: How many kilometers is there between A and B?

Solution: 24 km *2/(56 km -24 km) = 1.5 hours caught up with the cyclist.

Distance between Party A and Party B: 56km * 1.5 * 2 = 168km.

A: The distance between Party A and Party B is168km.

4. 12 after the motorcade set off, the correspondent chased them on a motorcycle and caught up with the motorcade at a distance of 9 kilometers from the starting point. Then, the correspondent immediately returned to the starting point and then returned to the chasing cycling team. When catching up again, it was just 18 km away from the starting point, trying to find the speed of the cycling team and motorcycle.

Suppose: the speed of the bicycle team is X km/min, and the speed of the motorcycle is Y km/min.

Solution: (18+9)/Y= 18/X, 3X=2Y.

12X=9(Y-X)/Y

8Y=9-6

Y=3/8 km/min

X =1/4km/min

A: The speed of cycling team is 1/4km/min, and that of motorcycle is 3/8km/min.

1. The distance between the two cities is 500 kilometers. A bus and a truck left the two cities at the same time. The average speed of buses is 55 kilometers per hour, and the average speed of trucks is 45 kilometers per hour. How many hours after the two cars left? 500/(55+45)=5 (hours)

2. Two cars leave from Party A and Party B at the same time. One car travels 56 kilometers per hour, and the other car travels 63 kilometers per hour. Four hours later, they met. How many kilometers is it between A and B? (56+63)×4=476 km

3. The bus and truck set off from two stations 275 kilometers apart at the same time and met within 2.5 hours on the way. It is known that the speed of passenger cars is 60 kilometers per hour, and how many kilometers per hour are trucks? 276/2.5-60 = 50km

4. At the same time, the two cars left relatively from two places 465 kilometers apart, and the distance between the two cars was still 120 kilometers after 4.5 hours. One car is 37 kilometers per hour, how many kilometers is the other car? (465-120)/4.5 = 39.7km.

Train c leaves from two cities at the same time. One train travels 60 kilometers per hour, and the other train travels 80 kilometers per hour. After 4 hours, it will still be 2 10 km. Find the distance between the two cities. (60+80) × 4+210 = 770km.

6. Team A and Team B dig canals together. Team A digs from east to west, while Team B digs from west to east. Team A digs 75 meters a day, which is 2.5 meters more than Team B. After eight days of cooperation, the difference between the two teams is 52 meters. What is the total length of this canal? (75=75-2.5)×8+52= 1232 (m)

7. The distance between Party A and Party B is 484 kilometers. A car travels from Party A to Party B. 1.5 hours later, a motorcycle travels from Party B to Party A, and meets an oncoming car four hours later. As we all know, cars travel 40 kilometers per hour. How many kilometers does the motorcycle travel per hour?

(484-40× 1.5)/4-40=66 (km)

8. The distance from Town A to Town B is 138km, and Zhang and Wang set out from two towns at the same time and walked in opposite directions. Zhang speed 13 km, Wang speed 12 km. When Wang traveled, he was delayed in repairing the car 1 hour, and then continued to travel. How many hours does it take from departure to meeting?

(138-13)/(13+12)+1= 6 (hours)

9. The distance between the two cities is 240 kilometers. Buses travel 50 kilometers per hour from city A to city B, and trucks travel 30 kilometers per hour from city B to city A. Two cars leave at the same time. How many kilometers are there in two hours? 240-(50+30) × 2 = 80km

10. Village A and Village B are opposite, with a distance of 3 1.2 km. Party A travels 4 kilometers per hour and Party B travels 4.8 kilometers per hour. When they met, the second line was 14.4 km. How many hours did A leave before B? (31.2-14.4)/4-14.4/4.8 =1.2 (hours)

1 1. The distance from Shanghai to Beijing is1035km. The first train from Shanghai to Beijing, the journey 185 km, 2.5 hours. At this time, the second train left Beijing for Shanghai, and the two trains met seven hours later. How many kilometers per hour is the B train?

( 1035- 185)/; 7-185/2.5 = 88km

12. Both the master and the apprentice process 800 parts at the same time, and the master processes 30 parts per hour, more than the apprentice 10. After the task is completed, how much more does the master handle than the apprentice? 10× [800/(30+30-10)] =160 (piece)

13. Two road repair teams opened a cave with a length of 13 14m from both sides of the mountain. The first team drives 8.8 meters every day, and the second team drives 8.6 meters every day. The first team worked for three days, and the remaining two teams rushed. How many days will it take before and after the opening of this cave?

(1314-8.8× 3)/(8.8+8.6)+3 = 77 (days)

14. It is estimated that it will take 40 minutes for a car to travel from A to B at a speed of 525 meters per minute. However, the machine broke down halfway and was repaired in 5 minutes. If we still arrive within the expected time, how many meters will the remaining distance be faster than the original speed per minute?

525× 40/2 (40/2-5)-525 =175 (m)

15. It took 36 hours for a car to go from A city to C city via B city. Walk 32 kilometers per hour from city A to city B, and walk 27 kilometers per hour from city B to city C. As we all know, the distance between the two cities is 64 0 kilometers. How many kilometers is the total distance?

640=27×(36-640/32)= 1072 (km)

16. Party A and Party B travel from two places in opposite directions at the same time. A travels 20 kilometers per hour, and B travels 18 kilometers per hour. When they met, they were 3 kilometers away from the midpoint. How many kilometers is the journey? (20+18) × [3× 2/(20-18)] =114 (km)

17. There is a train with a length of 260 meters. How many minutes does it take to cross the 6 10 meter bridge at a speed of 9 kilometers per hour?

(610+210)/(9000/60) = 5.8 (point)

18. Two bicycles of Party A and Party B are driving in opposite directions at the same place on a 6 1 km long loop. Car A leaves half an hour earlier than car B, and they meet three hours later. It is known that car A travels 12 kilometers per hour, and how many kilometers does car B travel per hour?

(61-12× 0.5)/(3-0.5)-12 =10 (km)

19. An express train and a local train leave from Party A and Party B at the same time, heading for each other, and meet after 5 hours. After the encounter, the express train continued to drive for 3 hours to reach B, and the slow train was known to be 48 kilometers per hour. How many kilometers is it between Party A and Party B?

(48+48×5/3)×5=640 km

20. The tortoise and the rabbit race. The tortoise runs 25 meters per minute and the rabbit runs 320 meters per minute. The rabbit thought it was faster than the tortoise, so it took a nap on the road. Results The tortoise reached the finish line 1.25 minutes earlier than the rabbit. How many minutes did Qiu Tu sleep on the road?

2000/25-2000/320+1.25 = 75 (points)

2 1. Party A and Party B go from East Village to West Village at the same time. After riding a bike to the West Village, Party A will return immediately and meet Party B at 760m from the West Village. B is known to walk for 8 minutes and 60 meters per minute. A How many meters does it take to ride a bike per minute? (760× 2+60× 8)/8 = 250m

Engineering problems:

First, the pursuit of work efficiency

1. One document is typed by Party A for 6 hours and Party B for 8 hours. How many fraction of this document does Party A complete every hour? B how many parts of this document do you finish every hour? How many parts of this document do these two people finish every hour?

2. It takes 10 hour for the truck to travel from place A to place B. How many times does the truck travel every hour?

3. A project can be completed in 5 days. How much can A complete this project every day?

2. Find the same completion time.

4. It takes Party A 6 hours, Party B 9 hours and Party A and Party B several hours to process a batch of parts.

5. For a project, team A has to work alone for 24 days and team B has to work alone for 16 days. How many days does it take if two teams work together?

6. There is a batch of goods at the station. Car A takes 6 hours, and car B can finish it in 9 hours. How many hours can two cars carry it at the same time?

3. Find out the time needed to complete some work

7. Team A 15 days can complete a project, while Team B 12 days. How many days does it take for Team A and Team B to complete the whole project together?

8. a manuscript It takes Xiao Fang six hours to finish typing alone, and Xiaohong eight hours to finish typing alone. How many hours did they work together to finish typing the manuscript?

9. It takes 10 days for Team A to dig tunnels, and 15 days for Team B to dig tunnels. How many days does it take for the two teams to jointly dig the tunnel now?

10. To build a highway, it takes 15 days for Team A to repair it alone, l2 days for Team B to repair it alone, 6 days for Team A first, and the rest will be repaired jointly by Team A and Team B. How many days will it take for Team A and Team B to repair it together?

1 1. A project can be completed by one person in group A within 9 days, by one person in group B within 12 days, and by both groups within 3 days. How many days will it take Team B to finish the rest?

12. To dig the foundation of a building, it takes 12 days for team A and 10 days for team B. Team B digs for 2 days first, and then both teams dig together. How many days will it take to complete?

13. The highway engineering team wants to build a bridge on the highway. It takes 6 months to build the bridge by itself, and it takes 10 months for Team B. After Team A has repaired it for 2 months, Team B will also participate in the construction. How many months will it take to complete?