Solution:
A's work efficiency =1/6-110 =115.
It takes1(115) =15 days to complete.
2. For a job, Party A will complete it in 5 hours 1, and Party B will complete half of the remaining tasks in 6 hours. Finally, Party A and Party B cooperated. How long will it take to finish the rest of the work?
Solution: A's work efficiency =( 1/4)/5= 1/20.
B completed (1-1/4) ×1/2 = 3/8.
Party B's work efficiency = (3/8)/6 =116.
The sum of the work efficiency of Party A and Party B =1/20+116 = 9/80.
At this point, 1- 1/4-3/8=3/8 has not been completed.
It takes (3/8)/(9/80)= 10/3 hours.
3. The construction team will complete a project in 30 days, with 18 people first and 12 days to complete 3/ 1 of the project. How many people will be added if it is completed on time?
Solution: Everyone's work efficiency = (1/3)/(12×18) =1/648.
It takes 30- 12= 18 days to finish on time.
Personnel required to finish the project on time (1-1/3)/(1/648×18) = 24 people.
Need to increase 24- 18=6 people.
4. Two people, Party A and Party B, process a batch of parts, with Party A processing 1.5 hours first, and then Party B processing. When the task is completed, Party A will complete five-eighths of this batch of parts. It is known that the efficiency ratio of Party A and Party B is 3:2. Q: How many hours does it take for Party A to process this batch of parts alone?
Solution: The working efficiency ratio of Party A and Party B is 3: 2.
That is, the ratio of workload is 3: 2.
B has completed 2/3 of A.
B Completed (1-5/8)=3/8.
Then when Party A and Party B work together, the amount of work completed is =(3/8)/(2/3)=9/ 16.
Therefore, it takes1.5/(5/8-9/16) =1.5/(1/6) = 24 hours.
5. A project needs the cooperation of Party A, Party B and Party C 13 days. If Party C has two days off, Party B will have to work four more days, or both parties will work 1 day. Q: How many days will it take for this project to be completed by Party A alone?
Solution: C for 2 days, B for 4 days.
In other words, it takes two days to do 1 day.
Then the workload of C 13 days is 2× 13=26 days.
Party B's 4 days is equivalent to 1 day.
That is, 3 days of B is equivalent to 1 day of A.
Armor alone takes a day to complete.
Then it takes three days for B to do it alone.
C it takes 3a/2 days for one person to do it.
According to the meaning of the question
1/a+ 1/3a+ 1/(3a/2)= 1/ 13
1/a( 1+ 1/3+2/3)= 1/ 13
1/a×2= 1/ 13
a=26
A It takes 26 days to do it alone.
Arithmetic: 13 days of C is equivalent to 26 days of B.
B doing 13+26=39 days is equivalent to A doing 39/3= 13 days.
So it takes a person 13+ 13=26 days to complete it.
7. Party A and Party B produce a batch of parts. The efficiency ratio of Party A and Party B is 2: 1. Co-shoot for three days, and Party B will shoot alone for the other two days. At this time, Party A has produced 14 more parts than Party B. How many parts are there in this batch?
Solution: Take the work efficiency of B as the unit 1.
Then a's work efficiency is 2.
B 2 days to complete 1×2=2.
Otsuichi * * * produces 1×(3+2)=5.
A * * * Output 2×3=6
So the work efficiency B = 14/(6-5)= 14/ day.
A's work efficiency = 14×2 = 28/ day.
A * * * has 28×3+ 14×5= 154 parts.
Or let the work efficiency of Party A and Party B be 2a/ day and A/ day respectively.
2a×3-(3+2)a= 14
6a-5a= 14
a= 14
A * * * has 28×3+ 14×5= 154 parts.
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.
1, A car and B car leave from AB at the same time. A walked 5/ 1 1 of the whole journey. If A drives at a speed of 4.5 kilometers per hour, B drives for 5 hours. How many kilometers are AB apart?
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 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 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.
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