Solution: AB distance = (4.5× 5)/(5/11) = 49.5 km.
2. A bus and a truck leave from Party A and Party B at the same time. The speed of a truck is four-fifths that of a bus. After a quarter of the journey, the truck and the bus met for 28 kilometers. How many kilometers is it between A and B?
Solution: The speed ratio of passenger cars and trucks is 5: 4.
Then the distance ratio when meeting is 5: 4.
When they met, it was 4/9 of the whole truck journey.
At this time, the truck has traveled all the way 1/4.
4/9- 1/4=7/36 from the meeting point.
Then the whole journey = 28/(7/36) = 144km.
3. Party A and Party B walk around the city, with Party A walking 8 kilometers per hour and Party B walking 6 kilometers per hour. Now both of them start from the same place at the same time. After B meets A, it will take another 4 hours to return to the original starting point. B How long does it take to go around the city?
Solution: The speed ratio of A and B = 8: 6 = 4: 3.
When they met, B walked 3/7 of the way.
Then 4 hours is 4/7 of the whole trip.
Therefore, the time spent on line B in a week =4/(4/7)=7 hours.
4. Party A and Party B walk from place A to place B at the same time. When Party A completes the whole journey of 1\4, Party B is still 640 meters away from B. When Party A completes the remaining 5\6, Party B completes the whole journey of 7\ 10. What's the distance between AB and place?
Solution: After A left 1/4, the remaining 1- 1/4=3/4.
Then the remaining 5/6 is 3/4×5/6=5/8.
At this time, a * * * left 1/4+5/8=7/8.
Then the distance ratio between Party A and Party B is 7/8: 7/ 10 = 5: 4.
So when A goes 1/4, B goes 1/4×4/5= 1/5.
Then AB distance =640/( 1- 1/5)=800 meters.
5. Two cars, A and B, start from A and B at the same time and drive in opposite directions. Car A travels 75 kilometers per hour, and car B takes 7 hours to complete the journey. Three hours after the departure of the two cars, the distance is15km. What is the distance between a and b?
Solution: Case A: Party A and Party B have not met yet.
3/7 of the 3-hour journey of the B train.
The three-hour journey is 75×3 = 225 kilometers.
AB distance = (225+15)/(1-3/7) = 240/(4/7) = 420km.
In one case, Party A and Party B have met.
(225- 15)/( 1-3/7)= 2 10/(4/7)= 367.5km。
6. One, two people should go this way. A It takes 30 minutes to walk and 20 minutes to walk. After walking for 3 minutes, A found that she didn't take anything, which delayed for 3 minutes. How many minutes does it take to walk from A to B?
Solution: A is 3+3+3=9 minutes later than B.
Think of the whole distance as 1.
Then the speed of a = 1/30.
Speed B = 1/20
When Party A packed up and set out, Party B had already left 1/20×9=9/20.
Then the distance between Party A and Party B is1-9/20 =11/20.
The sum of the speeds of Party A and Party B =1/20+1/30 =112.
Then meet again in (11/20)/(112) = 6.6 minutes.
7. two cars, a and b, start from place a and drive in the same direction. A walks 36 kilometers per hour and B walks 48 kilometers per hour. If car A leaves two hours earlier than car B, how long will it take for car B to catch up with car A?
Solution: distance difference = 36× 2 = 72km.
Speed difference = 48-36 = 12km/h
It takes 72/ 12=6 hours for car b to catch up with car a.
8. Party A and Party B respectively set out from ab, which is 36 kilometers apart, and walked in opposite directions. When Party A departs from A to 1 km, it has been in A until it finds something and returns immediately. After the goods were gone, he immediately went from place A to place B, where Party A and Party B met. He knew that Party A walked 0.5 kilometers more than Party B every hour and asked both of them to walk.
Solution:
A actually walked 36× 1/2+ 1× 2 = 20km when they met.
B walked 36× 1/2 = 18km.
Then A walked 20- 18 = 2km more than B.
Then the meeting time =2/0.5=4 hours.
So A = 20/4 speed = 5 km/h.
Speed B = 5-0.5 = 4.5km/h/h.
9. At the same time, two trains travel in opposite directions from two places 400 kilometers apart. The bus speed is 60 kilometers per hour, and the truck speed is 40 kilometers per hour. A few hours later, did the two trains meet at 100 km?
Solution: velocity sum = 60+40 =100 km/h.
There are two situations,
No encounter
Then the required time =(400- 100)/ 100=3 hours.
Met it.
Then the required time =(400+ 100)/ 100=5 hours.
10, A travels 9 kilometers per hour, and B travels 7 kilometers per hour. They walked back to back at the same time in two places 6 kilometers apart, and a few hours later they were separated by 150 kilometers.
Solution: velocity sum = 9+7 =16 km/h.
Then after (150-6)/16 =144/16 = 9 hours, the distance is150 kilometers.
1 1. Two cars A and B are driving in opposite directions at the same time from two places 600 kilometers apart. It is known that car A travels 42 kilometers per hour and car B travels 58 kilometers per hour. How many kilometers did B car travel when they met?
Solution:
Speed sum =42+58= 100 km/h
Meeting time =600/ 100=6 hours.
When they met, B traveled 58×6= 148 km.
or
The speed ratio of car A and car B = 42: 58 = 2 1: 29.
So when we met, B traveled 600×29/(2 1+29)=348 kilometers.
12, the two cars are facing each other, and meet in six hours. Four hours later, the bus arrived, and the van was still 188 kilometers away. How far is the distance between the two places?
Solution: treat the two cars as a whole.
65438+ 0/6 of the whole journey of two cars per hour
4 hour line 1/6×4=2/3
Then the whole journey =188/(1-2/3) =188× 3 = 564 km.
13. The distance between Party A and Party B is 600 kilometers. The bus and truck traveled in opposite directions from two places and met for six hours. As we all know, the speed of a truck is two-thirds that of a bus. What is the speed of the two cars?
Solution: the sum of the speeds of two cars = 600/6 =100 km/h.
Bus speed =100/(1+2/3) =100× 3/5 = 60 km/h.
Freight car speed = 100-60 = 40km/h
14. The rabbit and the kitten walked in opposite directions from A and B, which are 40 kilometers apart, respectively. Four hours later, they met for four kilometers. How long did it take to meet again?
Solution: velocity sum = (40-4)/4 = 9 km/h.
Then it will take 4/9 hours to meet.
15, car a and car b leave from a and b respectively. Car A travels 50 kilometers per hour and car B travels 40 kilometers per hour. Train A is earlier than train B 1 hour. What's the distance between the two places?
When car A reaches the finish line, car B is 40× 1 = 40km away from the finish line.
Car a travels 40 kilometers more than car B.
Then the time for a car to reach the finish line is 40/(50-40) = 4 hours.
Distance between the two places = 40× 5 = 200km.
16. Two cars leave from Party A and Party B at the same time and meet at 4 o'clock. The speed of the local train is three-fifths of that of the express train. When we met, the express train traveled 80 kilometers more than the local train. How far is the distance between the two places?
Solution: The speed ratio of the express train and the local train = 1: 3/5 = 5: 3.
When they met, the express train traveled 5/8 of the whole journey.
The local train covered three-eighths of the whole journey.
Then the whole journey = 80/(5/8-3/8) = 320km.
17, Party A and Party B set out from A and B respectively at the same time and walked towards each other. Party A walks every minute 100 meters, and Party B walks every minute 120 meters. Two hours later, they were150m apart. What is the shortest distance between a and b? What is the longest distance?
Solution: The shortest distance is that we have seen it, and the longest distance is that we have not seen it.
Speed sum =100+120 = 220m/min.
2 hours = 120 minutes
The shortest distance = 220×120-150 = 26400-150 = 26250m.
The farthest distance = 220×120+150 = 26400+150 = 26550m.
18, and the distance between Party A and Party B180km. A car is scheduled to travel from A to B for 4 hours, but it actually travels 5 kilometers per hour more than originally planned, so it can arrive a few hours earlier than originally planned.
Solution:
Original speed =180/4 = 45 km/h.
Actual speed = 45+5 = 50km/h.
Actual time = 180/50=3.6 hours.
4-3.6= 0.4 hours in advance
19, A and B start from AB at the same time. When they met, the distance they walked was 4: 3. After meeting, B is faster than A by 12km per hour, and A still keeps the original speed. As a result, the two cars arrived at the destination at the same time. It is known that B traveled 12 hours.
Solution: Let the speeds of Party A and Party B be 4a km/h and 3a km/h respectively.
therefore
4a× 12×(3/7)/(3a)+4a× 12×(4/7)/(4a+ 12)= 12
4/7+ 16a/7(4a+ 12)= 1
16a+48+ 16a=28a+84
4a=36
a=9
A =4×9=36 km/h speed.
AB distance = 36× 12 = 432km.
Arithmetic method:
Time after meeting = 12×3/7=36/7 hours.
Speed 12km, linear speed per second 12x36/7 = 432/7km.
When we met, A was more than B. 1/7.
Then the whole journey = (432/7)/( 1/7) = 432km.
20. Two cars, A and B, drive in opposite directions from two places 325 kilometers apart at the same time. The speed of A car is 52 kilometers per hour, and the speed of B car is 65438+0.5 times that of A car. When will the cars meet?
Solution: velocity b = 52×1.5 = 78 km/h.
325/(52+78)=325/ 130=2.5.
2 1, two cars, Party A and Party B, start from A and B at the same time and drive in opposite directions. A travels 80 kilometers per hour, and B travels 10% of the whole journey per hour. When B travels to 5/8 of the whole journey, Party A can reach B through 65438+ 0/6 of the whole journey. How many kilometers is it between A and B?
Solution: 5/8 of the whole journey of Bank B = (5/8)/(110) = 25/4 hours.
AB distance = (80× 25/4)/(1-kloc-0//6) = 500× 6/5 = 600 km.
22. Two cars of Party A and Party B leave the two places relatively at the same time. Car A travels 40 kilometers per hour and car B travels 45 kilometers per hour. When the two cars meet, the second car is 20 kilometers away from the midpoint. How many kilometers are the two places apart?
Solution: The speed ratio of A and B = 40: 45 = 8: 9.
Distance ratio between Party A and Party B = 8: 9.
When meeting, Party B made the whole journey of 9/ 17.
Then the distance between the two places = 20/(9/17-1/2) = 20/(1/34) = 680km.
23. Party A and Party B walk in opposite directions in two places at the same time, and meet at E. Party A continues to walk at B. Party B takes a rest 14 minutes, and then continues to walk at A. Party A and Party B turn back immediately after arriving at B and A respectively, and still meet at E. Know that A walks 60 meters per minute, B walks 80 meters per minute, and how many meters are there between A and B.
Solution: treat the whole process as a unit 1.
The speed ratio between Party A and Party B is 60: 80 = 3: 4.
The distance a of point E is 3/7 of the whole journey.
When we meet for the second time, one * * * is three times.
After resting 14 minutes, A walked 60× 14=840 meters.
After the first meeting, B left 3/7×2=6/7.
Then the distance traveled by A is 6/7×3/4=9/ 14.
In fact, A left 4/7×2=8/7.
Then during B's rest, A left 8/7-9/ 14= 1/2.
Then the whole journey = 840/( 1/2) = 1680m.
24. Two trains, A and B, leave relatively from AB at the same time. When they meet, the distance ratio between A and B is 4: 5. It is known that train B travels 72 kilometers per hour, and it takes 10 hour for train A to complete the whole journey. How many kilometers are there between AB and AB?
Solution: The ratio of the distance left when meeting is 4: 5.
Then the distance ratio is 5: 4.
The time ratio is equal to the inverse ratio of the distance ratio.
Distance ratio between Party A and Party B = 5: 4.
The time ratio is 4: 5.
Then it takes 10×5/4 = 12.5 hours for line B to complete the journey.
Then AB distance =72× 12.5=900 km.
25. Party A and Party B walk from A and B to each other at the speed of 4 kilometers and 5 kilometers per hour respectively. After meeting, they walked on. How many kilometers is there between A and B if A walks from the assembly point for another two hours and arrives at B?
Solution: The distance ratio when A and B meet = the speed ratio = 4: 5.
Then when they meet, A is 5/9 of the distance from the destination.
So AB distance = 4× 2/(5/9) = 72/5 = 14.4km.
26. Passenger cars and trucks depart from Party A and Party B relatively simultaneously. After meeting on the way, they moved on. They returned immediately after they arrived at each other's departure place. They met for the second time on the road. The distance between the two venues is120km. The bus travels 60 kilometers per hour and the truck travels 48 kilometers per hour. How many kilometers is the distance between Party A and Party B?
Solution: The speed ratio of passenger cars and trucks = 60: 48 = 5: 4.
Think of the whole distance as 1.
Then the first intersection is 1×5/(5+4)=5/9 from A.
The second encounter is three complete journeys.
Then the second intersection from B is1× 3× 5/9-1= 5/3-1= 2/3.
That is, the distance from A is 1-2/3= 1/3.
So the distance between Party A and Party B =120/(5/9-1/3) =120/(2/9) = 540 km.
27. A bus and a truck set off from A and B at the same time and met for 5 hours. After the rendezvous, the two cars continued to drive forward for three hours. At this time, the bus distance b is180km, the truck distance a is 2 10/0km, and how many kilometers is AB?
Solution: 65438+ 0/5 of the whole journey of two cars per hour.
Then 3 hours 1/5×3= 3/5 of the whole journey.
So the whole journey = (180+210)/(1-3/5) = 390/(2/5) = 975 km.
28. Party A and Party B started from AB, and the speed of Party A was 4/5 of that of Party B. After arriving at Party B and Party A, Party A returned to AB, and the speed of Party A increased by 1/4, and that of Party B increased by 1/3. It is understood that the distance between the two meeting points A and B is 34 kilometers. What's the distance between AB?
Solution: Take the whole journey as the unit 1.
Because time is constant, the distance ratio is the speed ratio.
Distance ratio of Party A and Party B = speed ratio = 4: 5
B's speed is fast, B reaches point A, and A travels 1×4/5=4/5.
At this time, Party B speeds up 1/3, so the speed ratio of Party A and Party B is 4: 5× (1+ 1/3) = 3: 5.
A left 1-4/5= 1/5, so b left (1/5)/(3/5)= 1/3.
At this time, A accelerates and the speed ratio changes from 3: 5 to 3 (1+ 1/4): 5 = 3: 4.
The distance between Party A and Party B is 1- 1/3=2/3.
When meeting, Otsuichi left1/3+(2/3) × 4/(3+4) =1/3+8/21= 5/7.
That is, 5/7 of the distance a.
The meeting point for the first time is 4/9 of the distance a.
Then AB distance = 34/(5/7-4/9) = 34/(17/63) =126km.
29. Xiaoming gets up at 5 o'clock and looks at the clock. The word 6 is right in the middle of the hour hand and the minute hand (that is, the distance from the two hands to 6 is equal). What time is five o'clock?
Solution: Suppose it's 5 a.m..
The minute hand moves 1 grid every minute, so the hour hand moves 5/60 =112 grid every minute.
According to the meaning of the question
a-30=5-a/ 12
13/ 12a=35
A=420/ 13 minutes ≈32 minutes 18 seconds.
It's 5: 32, 18 seconds.
Here, 30 and 5 represent 30 squares and 5 squares, that is, 1 square on the clock face.
As a special travel problem.
30. A cruise ship is sailing on the Yangtze River. It takes 3 hours to sail from Port A to Port B, and 4 hours and 30 minutes to return. How many hours does it take for an empty bucket to drift the same distance only by the current? Solution: downstream velocity 1/3, upstream velocity 1/4.5 = 2/9.
Flow velocity = (1/3-2/9)/2 =118.
Need1/(118) =18 hours.
involve