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Math assistant in the fifth grade of primary school
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.

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 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.

1, a project, a team alone for 20 days to complete, b team alone for 30 days to complete, now b team for 5 days, the rest by a team and b team cooperation, how many days to complete?

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.