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.
2. 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。
1. Both 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. How many minutes' walk can you meet 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.
4. Two cars, A and B, start from 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.
Party A and Party B start from ab, which is 36 kilometers apart, and go 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.
6. Two trains run in opposite directions from two places 400 kilometers apart at the same time. The bus speed is 60 kilometers per hour, and the truck speed is 40 kilometers per hour. Two hours' drive, do the two trains meet at100km?
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.
7. 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.
8. Car A and car B are driving in the opposite direction from two places 600 kilometers apart at the same time. It is known that car A travels 42 kilometers per hour and car B travels 58 kilometers per hour. How many kilometers did B car travel when they met?
Solution:
Speed sum =42+58= 100 km/h
Meeting time =600/ 100=6 hours.
When they met, B traveled 58×6= 148 km.
or
The speed ratio of car A and car B = 42: 58 = 2 1: 29.
So when we met, B traveled 600×29/(2 1+29)=348 kilometers.
9. Two cars face each other, meet in 6 hours, and then the bus will arrive in 4 hours, truck 188 km. How far is the distance between the two places?
Solution: treat the two cars as a whole.
65438+ 0/6 of the whole journey of two cars per hour
4 hour line 1/6×4=2/3
Then the whole journey =188/(1-2/3) =188× 3 = 564 km.
10. The distance between Party A and Party B is 600 kilometers, and the bus and truck run in opposite directions from the two places and meet for 6 hours. As we all know, the speed of a truck is two-thirds that of a bus. What is the speed of the two cars?
Solution: the sum of the speeds of two cars = 600/6 =100 km/h.
Bus speed =100/(1+2/3) =100× 3/5 = 60 km/h.
Freight car speed = 100-60 = 40km/h
1 1. Rabbits and kittens walk in opposite directions from A and B, which are 40 kilometers apart. Four hours later, they met for four kilometers. How long did it take to meet?
Solution: velocity sum = (40-4)/4 = 9 km/h.
Then it will take 4/9 hours to meet.
12. A train passed a 900-meter-long railway bridge, and it took 1 minute and 25 seconds to get from the front bridge to the rear bridge. Then the train passed through a tunnel with a length of 1800 meters at the same speed, and it took 2 minutes and 40 seconds to get the speed of the train and the length of the car body.
2 minutes and 40 seconds = 160 seconds
1 min 25 seconds =85 seconds
Train speed = (1800-900)/(160-85) = 900/75 =12m/s.
Analysis: the two processes are the same, both entering from the front and leaving from the rear, so the distance/multiple use time of the second time is more than the first time = the speed of the train.
body = 12×85-900 = 1020-900 = 120m。
It is relatively easy to ask for a car body.
13. From A to B, go uphill first and then downhill. The speed of the car is 20 kilometers per hour uphill and 35 kilometers per hour downhill. It takes 9 hours for a car to travel from A to B, and 7.5 hours to return from B to A ... How many kilometers are uphill and downhill respectively?
Solution: This problem needs to understand an implicit condition, that is, uphill distance = downhill distance.
Distance, time ratio = inverse ratio of speed ratio.
So uphill time: downhill time = downhill speed: uphill speed = 35: 20 = 7: 4.
Total time =9+7.5= 16.5 hours.
So uphill time =16.5× 7/11=10.5 hour.
The distance between Party A and Party B =20× 10.5=2 10 km.
At this time, we are considering the problem that chickens and rabbits are in the same cage.
Assuming that the whole city is uphill, the distance between Party A and Party B is = 20× 9 = 180km.
2 10- 180 = 30km shorter than the time.
Then downhill time =30/(35-20)=2 hours.
Then the uphill distance = 20× (9-2) = 140km.
Downhill distance = 2 10- 140 = 70km.
14. A project, with group A alone for 20 days and group B alone for 30 days. Now Team B has done it for five days, and the rest will be done 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.
15. It takes 15 days for Party A to complete a project, 15 days for Party B, 20 days for Team C, and 6 days for Team A to leave because of something. 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.
Selection and solution of mathematics application problems in primary schools
1, Xiaohua read a story book with a page of 120, and read the whole book on the day of 1/3. (1) 1 How many pages did he read that day? (2) How many pages are left unread?
Answer:120×1/3 = 40 (page)120-40 = 80 (page) or120× (1-kloc-0//3).
2. Xiaohua read a story book with a page of 120, read 1/3 of the whole book on the first day, and read 1/4 of the whole book the next day.
(1) 1 How many pages did you read this day? (2) How many pages did you read the next day? (3) How many pages have not been read?
Answer: (1)120×1/3 = 40 (page) (2)120×1/4 = 30 (page).
(3) 120-40-30 = 50 (page) or120× (1-1/4) = 50 (page).
Xiaohua read a story book with 120 pages. On day 1/3, he read the rest 1/4 the next day. How many pages did he read the next day?
120× 1/3=40 (page) 120-40 = 80 (page) 80× 1/4=20 (page)
Or (1—1/3) ×1/4 =1/6120×1/6 = 20 (page).
Xiaohua read a story book. On 1 day, he read 1/3 of the whole book, and the next day he read the rest 1/4, leaving six pages unread.
(1) How many pages does this story book have?
Answer: (1-1/3) ×1/4 =1/66 ÷ (1-1/3-1/6).
(2) How many more pages were read on 1 day than the next day?
Answer:12× (1/3—1/6) = 2 (page)
Xiaohua read a story book. On 1 day, he read 1/3 of the whole book. The next day, he read the rest 1/4. On 1 day, he read 20 pages more than the next day.
(1) How many pages does this story book have?
Answer: (1-1/3) ×1/4 =1/6 20 ÷ (1/3-1/6) =1.
(2) How many times the number of pages read on 1 day is that on the second day?
Answer: 1/3÷ 1/6=2 (times)
6. Xiaohua read a story book. On the first 1 day, he read 1/3 of the book. On the second day, he read 20 pages. On the third day, he read the rest 1/4, with 3/8 of the book still unread. How many pages does this story book have?
Answer:
7. A motorcycle completed a journey of 60 kilometers at an average speed of 20 kilometers per hour. On the way home, its average speed is 30 kilometers per hour. What is the average speed of the motorcycle during the whole round trip?
8. A batch of goods arrived at the station. On the first day, all the goods of 1/3 and 20 tons were shipped, and on the second day, all the goods of 1/4 and 30 tons were shipped. There are still 30 tons of goods in the station at this time. How many tons are there in this batch?
9. There is a batch of goods at the station. On the first day 1/3, the whole cargo was 20 tons short, and on the second day 1/4, the whole cargo was much 10 ton. There are still 70 tons of goods in the station at this time. How many tons are there in this shipment?
10. There is a batch of goods at the station. On the first day, all the goods were transported 20 tons, and on the second day, all the goods were transported 1/4, which was 10 tons. At this time, there are 1 10 tons of goods in the station. How many tons are there in this shipment?
1 1. There is a batch of goods at the station. On the first day, all the goods of 20 tons13 were shipped more, and on the second day, all the goods of 25 tons12 were shipped less. At this time, there are 37 tons of goods in the station. How many tons are there in this shipment?
12. There is a batch of goods at the station. 1/3 of all the goods were transported for the first time, and less than 3/4 of all the goods were transported for the second time 16 tons. At this time, all the goods were shipped out. How many tons are there in this shipment?
13. There is a batch of goods at the station. On the first day, two-thirds of the goods were transported less than 28 tons, and on the second day, three-quarters of the goods were transported less than 52 tons, which was just finished. How many tons are there in this shipment?
14. The chemical fertilizer plant plans to produce a batch of chemical fertilizers. On the first day, 1/6 of all tasks was generated, on the second day, 1/4 of the remaining tasks was generated, and on the third day, 1/5 of the remaining two days was generated. Therefore, there are still 50 tons unfinished. How many tons of fertilizer does the fertilizer plant plan to produce?
15, mother bought eggs and duck eggs ***2 1, of which duck eggs accounted for 3/7; Later, my mother bought some duck eggs, accounting for 7/ 13 of the total eggs. Later, my mother bought some duck eggs.
16. There is a pile of bricks. After moving out, 1/4 brought another 360 bricks. At this time, the pile of bricks was 20% more than before. How many bricks are there in this pile?
17, the master and the apprentice made 200 parts together, and the master made 25% more parts than the apprentice 14. How many parts did the apprentice make?
18, there is a mountain road. A car goes up the mountain at a speed of 30 kilometers per hour and returns from the original road at a speed of 50 kilometers per hour. What is the average speed of cars going up and down the mountain?
19, mentoring processes a batch of parts, and the number of parts processed by the master is 25 more than the total 1/2, and the number of parts processed by the apprentice is 1/3 of that of the master. How many parts are there in this batch?
20. A, B and C all delivered a batch of goods. Team A delivered 65,438+0/4 of the goods, team B delivered a part, and team C delivered 65,438+0/3 of the goods, and all of them were shipped out. It is known that Team A shipped less 10 tons than Team C. How many tons did Team B ship?
2 1, Party A and Party B go to the bookstore to buy books and take them to 54 yuan. Party A spends 75% of its own money, Party B spends 4/5 of its own money, and the rest is exactly the same. How much did Party A and Party B originally bring?
22. Team A and Team B jointly built a 2500-meter-long highway. Team A completed 2/3 of the assigned tasks, while Team B completed 3/4 and 50m of the assigned tasks, leaving 700m unresolved. How many meters are the tasks assigned by the two teams?
There are apple trees and pear trees in the orchard. The apple tree area is 4 hectares more than the total area 1/2, and the pear tree area 1/2. How many hectares of two kinds of trees have been planted?
24. There are two piles of coal in midsummer Chemical General Factory, weighing 2268 kilograms. Take out 2/5 of pile A and pile B of 1/4 * *, weighing 708kg. How many kilograms are there in raw coal piles A and B respectively?
25. Two workers, Party A and Party B, * * * simultaneously process 140 parts. A has completed 80% of his tasks, and B has completed 75% of his tasks. At this point, 32 parts of A and B * * * remain unfinished. How many parts do workers A and B need to make?
26. The master and the apprentice * * * processed 540 parts, the master processed 3/4 of his assigned tasks, and the apprentice processed 80% of the assigned tasks, and the remaining tasks were exactly equal. How many copies did the master and apprentice get respectively?
27. The school bought 220 books of * * *, took out 4 books of Class A 1/and 50 books of Class B1/5 * *, and lent them to fifth-grade students (1). How many books did A and B buy back?
28. The school bought a batch of books, among which literature and art books accounted for 4/9, mathematics books accounted for the rest 18/25, and the known mathematics books were 20 less than literature and art books. How many books are there in this batch?