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.
32. Both cars of Party A and Party B travel from place A to place B, with car A traveling 65 kilometers per hour and car B traveling 42 kilometers per hour. B train starts two hours before departure. A few hours later, car A overtook car B. ..
Solution: distance difference =42×2=84 km.
Speed difference = 65-42 = 23km
After 84/23=3 and 15/23 hours ≈3.65 hours.
Car a overtook car B.
33. Two cars, A and B, leave from A and B relatively at the same time and meet in four hours. After meeting, Party A will drive to B for three hours. If car A is 20 kilometers faster than car B per hour, how many meters is there between A and B?
Solution: It takes 4+3=7 hours for a car to travel all the way.
In other words, when they met, A walked 4/7 of the whole journey.
Then B walked 3/7 of the way.
Speed ratio of Party A and Party B = distance ratio = 4/7: 3/7 = 4: 3 = 1: 3/4.
So the speed of a car = 20/(1-3/4) = 80 km/h.
AB Distance =80×7=560 km
34. Two cars, A and B, leave from A and B relatively at the same time and meet in four hours. After meeting, Party A will drive to B for three hours. If car A is 20 kilometers faster than car B per hour, how many meters is there between A and B?
Solution: It takes 4+3=7 hours for a car to travel all the way.
In other words, when they met, A walked 4/7 of the whole journey.
Then B walked 3/7 of the way.
Speed ratio of Party A and Party B = distance ratio = 4/7: 3/7 = 4: 3 = 1: 3/4.
So the speed of a car = 20/(1-3/4) = 80 km/h.
AB Distance =80×7=560 km
35. Two cars leave from Party A and Party B at the same time. Car A travels 48 kilometers per hour, and car B travels 54 hours per hour. When they met, the two cars were 36 kilometers away from the midpoint. How many kilometers is it between Party A and Party B?
Solution: The speed ratio of car A and car B = 48: 54 = 8: 9.
Then when we met, a car took the whole journey for 8/ 17.
So the distance between Party A and Party B is = 36/(1/2-8/17) = 36/(1/34) =1224km.
36. Two cars, A and B, leave from A and B at the same time and drive in opposite directions. When starting, the speed ratio of Party A and Party B is 3 to 2. After the meeting, Party A's speed decreased by 20% and Party B's speed increased by 20%. So, when A arrives at B, B is still 100 km away from A ... How many kilometers away is AB?
Solution: We met for the first time at a distance of 3/5.
At this time, the speed ratio between Party A and Party B becomes 3× (1-20%): 2× (1+20%) = 2.4: 2.4 =1:1.
Then we met for the second time, and A traveled 2/5 to B.
However, the distance from B to A is 3/5-2/5 = 1/5.
So AB distance = 100/( 1/5)=500 km.
37. An express train and a local train leave from both parties at the same time. After they met, the two cars continued to drive. The express train arrives at Party A, and the local train returns immediately after arriving at Party B..
The second meeting place is 0/40km away from A/KLOC, and the speed ratio of express train to local train is 4: 3. How many kilometers is it between A and B?
Solution: Slow driving 3/7×3=9/7.
Then AB distance =140/(9/7-1) = 490 km.
38.A and B walk from A and B at the same time, meet at the same speed five minutes later, and A arrives at B four minutes later. At this time, B is 80 meters away from A/KLOC-0 ... How many meters is there between A and B?
Solution: Time spent on the whole journey of Line A =5+4=9 minutes.
Then the distance from the first encounter with line A is 5/9 of the whole journey.
B did 4/9.
The distance ratio between Party A and Party B is 5/9: 4/9 = 5: 4.
So A went to B, and B did 1×4/5=4/5.
Then AB distance =180/(1-4/5) =180/(1/5) = 900 meters.
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