I don't know the topic, I don't know the grade, but I found some topics by experience and accumulated them myself. I hope it will be helpful to your study.

1. A project takes Party A 6 days to complete, and Party B alone 10 days. How many days does it take for Party A to do it alone?

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 both parties work together, and the completed workload 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.

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 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. 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.