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.
The construction team will finish a project in 30 days, 18 people first, 12 days to finish 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.
6. Solution: Party B makes 60 sets, and Party A makes 60/(4/5)=75 sets.
A three days 165-75=90 sets.
A's working efficiency =90/3=30 sets.
B Processing 30×4/5=24 sets per day.
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.
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.
15. For a project, Party A will do it for 3 days first, and then Party B will join in. Two-thirds of the projects completed after 4 days are 1 and three-quarters of the projects completed after 10. A was transferred because of some things, and B did the rest. How many days did a * * * do?
Solution: according to the meaning of the problem
The cooperation between Party A and Party B began in 4 days13 and ended in 3/4 days 10.
So the cooperation between Party A and Party B is10-4 = 3/4- 1/3=5/ 12 in 6 days.
Therefore, the work efficiency of both parties is =(5/ 12)/6=5/72.
Then the working efficiency a = (1/3-5/72× 4)/3 = (1/3-5/18)/3 =1/54.
Party B's work efficiency = 5/72-1/54 =11/216.
Then B needs to complete the remaining (1-3/4)/(11/216) = 54/11day.
A * * * made 3+10+54/1=17 and10//day.
16, both parties made the same parts. /kloc-After 0/6 days, Party A needs 64 B and 384 B to complete it. The work efficiency of Party B is 40% less than that of Party A, so how can we find the efficiency of Party A?
Solution: Let the working efficiency of A be A/ day, and then B be (1-40%)A = 0.6a/ day.
According to the meaning of the question
16a+64=0.6a× 16+384
16×0.4a=320
0.4a=20
A=50/day
A's work efficiency is 50/ day.
Arithmetic method:
B does 40% less than A every day.
Then 16 days is 384-64= 320 less.
Do 320/ 16 = 20 less every day.
Then the working efficiency of A = 20/40% = 50/ day.
17, Master Zhang has a rest every six days 1 day, and Master Wang has a rest every five days for two days. For an existing project, Master Zhang needs 97 days and 75 days. If two people cooperate, how many days does a project take?
Solution:
97 divided by 7 equals 13, leaving 6 13 * 6 = 78, 78+6 = 84 working days.
75 divided by 7 equals 10,5,10 * 5 = 50,50+5 = 55 working days.
Master Zhang completes 1/84 every working day and 6/84 =114 every week.
Master Wang completes 1/55 every working day and 5/55 =11/every week.
Two people work together to complete 139/4620 every working day and 25/ 154 every week.
Six weeks to complete 150/ 154, leaving 4/ 154.
(4/ 154)/( 139/4620)= 120/ 139
So, six weeks and one day, 43 days.
I still have application questions, and other questions can be found or downloaded from Baidu Library.