Solution: Let the speeds of Party A and Party B be 4a km/h and 3a km/h respectively.
therefore
4a× 12×(3/7)/(3a)+4a× 12×(4/7)/(4a+ 12)= 12
4/7+ 16a/7(4a+ 12)= 1
16a+48+ 16a=28a+84
4a=36
a=9
A =4×9=36 km/h speed.
AB distance = 36× 12 = 432km.
Arithmetic method:
Time after meeting = 12×3/7=36/7 hours.
Speed 12km, linear speed per second 12x36/7 = 432/7km.
When we met, A was more than B. 1/7.
Then the whole journey = (432/7)/( 1/7) = 432km.
20. Two cars, A and B, drive in opposite directions from two places 325 kilometers apart at the same time. The speed of A car is 52 kilometers per hour, and the speed of B car is 65438+0.5 times that of A car. When will the cars meet?
Solution: velocity b = 52×1.5 = 78 km/h.
325/(52+78)=325/ 130=2.5.
2 1, two cars, Party A and Party B, start from A and B at the same time and drive in opposite directions. A travels 80 kilometers per hour, and B travels 10% of the whole journey per hour. When B travels to 5/8 of the whole journey, Party A can reach B through 65438+ 0/6 of the whole journey. How many kilometers is it between A and B?
Solution: 5/8 of the whole journey of Bank B = (5/8)/(110) = 25/4 hours.
AB distance = (80× 25/4)/(1-kloc-0//6) = 500× 6/5 = 600 km.
22. Two cars of Party A and Party B leave the two places relatively at the same time. Car A travels 40 kilometers per hour and car B travels 45 kilometers per hour. When the two cars meet, the second car is 20 kilometers away from the midpoint. How many kilometers are the two places apart?
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. How to find 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.
3 1. It takes 30 minutes for buses and trucks to leave from A to B. As a result, trucks arrive earlier than buses 1 hour. If the distance between A and B is 360 kilometers, the speed of the bus is 3/4 of that of the truck. What are the speeds of trucks and buses respectively?
Solution: If the bus leaves at the same time and arrives later than the truck, it will be 1 hour 30 minutes = 1.5 hours.
The speed ratio of passenger cars and trucks is 3: 4.
Time ratio = 4: 3
Therefore, the whole bus journey time = 1.5/( 1-3/4)=6 hours.
So the bus speed = 360/6 = 60 km/h.
Truck speed = 60/(3/4) = 80km/h.
Besides, if necessary, please give me an email address.