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 it takes 7 hours for car B 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. I walked for a few minutes before I saw him.
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 another 14, rabbits and kittens walk in opposite directions from A and B, which are 40 kilometers apart. Four hours later, they met at 4 kilometers. How long before we 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 100 meters per minute, and Party B walks 120 meters per minute. 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 4 km/h and 3 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. Car A travels 52 kilometers per hour, and the speed of car B is 1.5 times that of car A. 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.
(11/20)/(112) = Meet in 6.6 minutes.
8. For a project, the time for Party B to complete the project alone is twice that of Party A's team; It takes 20 days for Team A and Team B to cooperate to complete the project. The daily work cost of Team A is 1 1,000 yuan, and Team B is 550 yuan. From the above information, which company should I choose from the perspective of saving money? How much should be paid to the construction team?
Solution: The sum of the work efficiency of both parties = 1/20.
Working time ratio of Party A and Party B = 1: 2.
Then the work efficiency ratio of Party A and Party B is 2: 1.
So the working efficiency A = 1/20×2/3= 1/30.
Party B's work efficiency =1/20×1/3 =1/60.
A it takes one person 1/( 1/30)=30 days.
B It takes1(1/60) = 60 days to complete it alone.
A need to complete it alone1000× 30 = 30,000 yuan.
B alone needs 550× 60 = 33,000 yuan.
The cooperation needs of Party A and Party B are (1000+550) × 20 = 31000 yuan.
obviously
A needs the least money to finish it alone.
Choose a, you need to pay 30000 yuan for this project.
9. For a batch of parts, if Party A and Party B work together for 5.5 days, it can exceed 0. 1 of the batch of parts. Now Party A works for 2 days, then Party A cooperates for 2 days, and finally Party B works for 4 days to complete the task. If Party B works alone, how many days can this batch of parts be completed?
Solution: treat all parts as a unit 1.
Then the sum of the work efficiency of Party A and Party B = (1+0.1)/5.5 =1/5.
The whole process is that A works 2+2=4 days.
B working 2+4=6 days.
It is equivalent to 4 days of cooperation between Party A and Party B, and 1/5×4=4/5 is completed.
Then B does it alone for 6-4=2 days 1-4/5= 1/5.
So it takes 2/( 1/5)= 10 days for B to complete it alone.
10, there is a project to be completed within the specified date. If Team A does it alone, it will be finished on schedule. If Team B does it alone, it will take more than 5 days to finish. Now Team A and Team B have been working together for three days, and the rest of the projects are completed by Team B alone as planned. How many days is the specified date?
Solution: 3 days of A is equivalent to 5 days of B.
The work efficiency ratio of Party A and Party B is 5: 3.
Then the ratio of completion time between Party A and Party B is 3: 5.
So it takes 3/5 time for A to complete.
So it takes 5/(1-3/5) = 5/(2/5) =12.5 days for B to complete it alone.
Specified time = 12.5-5=7.5 days.
1 1. A project will be completed in 20 days by team A and 30 days by team B. Now team B will finish it in five days, and the rest will be completed by team A and team B. How many days will it take?
Solution: B completed 5× 1/30= 1/6 in 5 days.
The work efficiency of Party A and Party B =1/20+1/30 =1/6.
Then (1-1/6)/(1/6) = (5/6)/(1/6) = 5 days.
12. It takes 15 days for Party A to complete a project, 15 days for Party B, and 20 days for Team C. The three teams work together, and Team A has left because of something. It took six days. How many days did Team A actually work?
Solution: the sum of the working efficiency of ethylene and propylene =115+1/20 = 7/60.
Do both B and C for 6 days, and finish 7/60×6=7/ 10.
A complete1-7/10 = 3/10.
Then A actually made it (3/10)/(110) = 3 days.
12. It takes 4 hours for Party A, 2.5 hours for Party B and 5 hours for Party C to process a part. There are currently 187 pieces to be processed. If it is stipulated that three people spend the same amount of time to finish it, how many parts will each person have to process?
Solution: It takes 1/4 hours, 2/5 hours and 1/5 hours to process1parts respectively.
Then the completion time =187/(1/4+2/5+1/5) =187/0.85 = 220 hours.
Then a treatment 1/4×220=55.
B processing 2/5×220=88 pieces.
C treatment 1/5×220=44.
13. A project was completed by Party A on May1,and then completed by both parties, which took 16 days. It is known that the efficiency ratio of Team A and Team B is 2: 3. How many days does it take for Team A and Team B to finish this project independently?
Solution: The working efficiency of Party A and Party B = (1-1/5)/16 = (4/5)/16 =1/20.
A's work efficiency =1/20× 2/(2+3) =1/50.
Party B's work efficiency =1/20-1/50 = 3/100.
Then it takes1(1/50) = 50 days for A to complete it alone.
It takes1(3/100) =100/3 days =33 days and 1/33 days.
14, a project, a team of 20 people do it alone for 25 days. If it takes 20 days to complete, how many people need to be added?
Solution: Take everyone's workload as the unit 1.
It is also necessary to increase/kloc-0 /× 25× 20/(/kloc-0 /× 20)-20 = 25-20 = 5 people.
for reference only