1. Two cars, A and B, leave from AB at the same time. A traveled 5/11 of the whole journey. If A traveled 4.5 kilometers per hour, B traveled 5 hours. How many kilometers are there between AB?

Solution: AB distance = (4.5×5)/(5/11)=49.5 kilometers

2. A passenger car and a car Two trucks leave from two places, A and B, in opposite directions at the same time. The speed of the truck is four-fifths that of the passenger car. After traveling a quarter of the entire distance, the truck travels another 28 kilometers to meet the passenger car. How many kilometers are there between places A and B?

Solution: The speed ratio of passenger cars and trucks is 5:4

Then the distance ratio when they meet = 5:4

The distance traveled by the truck when they meet 4/9

At this time, the truck has traveled 1/4 of the entire journey

It is still 4/9-1/4=7/36 from the meeting point

Then the whole distance = 28/(7/36) = 144 kilometers

3. Two people, A and B, walk around the city. A travels 8 kilometers per hour and B travels 6 kilometers per hour. Now two people start from opposite sides at the same time. After B meets A, they will travel another 4 hours to return to the original starting point. How long does it take for B to circle the city?

Explanation: The speed ratio of A and B = 8: 6 = 4: 3

When they met, B traveled 3/7 of the entire journey

Then 4 hours is the entire journey 4/7

So the time it takes for B to travel in one week = 4/(4/7) = 7 hours

4. Two people, A and B, walk from point A to point B at the same time. When A has walked 1\4 of the whole distance, B is still 640 meters away from B. When A has walked the remaining 5\6, B has walked 7\10 of the whole distance. How many meters is the distance between AB and B?

Explanation: After A has moved 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 and B have walked 1/4+5/8=7/8

Then the distance ratio of A and B = 7/8: 7/10=5 : 4

So when A walks 1/4 of the whole distance, B walks 1/4×4/5=1/5

Then distance AB = 640/(1 -1/5) = 800 meters

5. Two cars A and B drove out from A and B at the same time, heading towards each other. Car A travels 75 kilometers per hour, and car B takes 7 hours to complete the journey.

The distance between the two cars is 15 kilometers after 3 hours of driving. How many kilometers are there between places A and B?

Explanation: A situation: A and B have not met yet

3/7 of the whole journey of car B’s 3-hour trip

A’s 3-hour trip is 75×3 =225 kilometers

AB distance = (225+15)/(1-3/7)=240/(4/7)=420 kilometers

One situation: A and B have met

(225-15)/(1-3/7)=210/(4/7)=367.5 kilometers

6. A, two people want to meet After walking this road, A has to walk for 30 minutes and has already walked for 20 minutes. After walking for 3 minutes, A finds that he has not taken something. He is delayed by 3 minutes in taking the things. How many more minutes will A go to meet him?

Consider the entire distance as unit 1

Then A’s speed = 1/30

B’s speed = 1/20

When A takes the things and sets off, B has already left 1/20×9=9/20

Then A and B move together The distance of 1-9/20=11/20

The speed of A and B =1/21/30=1/12

Then there is (11/20)/ (1/12) = 6.6 minutes of encounter

7. Two cars A and B start from point A and travel in the same direction. A travels 36 kilometers per hour and B travels 48 kilometers per hour. If car A leaves 2 hours earlier than car B, how long does it take for car B to catch up with car A?

Solution: Distance difference = 36 × 2 = 72 kilometers

Speed ??difference = 48-36 = 12 kilometers/hour

Car B needs 72/ 12=6 hours to catch up with A

8. A and B set out from two places a, which are 36 kilometers apart, at the same time and walked towards each other. When A set out from place a to 1 kilometer away, he found something In the past, when they were at place a, they would return immediately, and immediately travel from place a to place b after taking the items. In this way, A and B happen to meet at the end points of places a and b. It is also known that A walks 0.5 more hours per hour than B. Kilometers, what are the speeds of A and B?

Solution:

A actually walked 36×1/2+1×2=20 kilometers when they met

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B walked 36×1/2=18 kilometers

Then A walked 20-18=2 kilometers longer than B

Then the time it took to meet =2/0.5=4 hours

So A’s speed=20/4=5 kilometers/hour

B’s speed=5-0.5=4.5 kilometers/hour

9. Two trains run towards each other from two places 400 kilometers apart at the same time. The passenger train travels 60 kilometers per hour and the truck travels 40 kilometers per hour. After running for a few hours, the two trains meet and are 100 kilometers apart. rice?

Solution: The sum of speeds = 640 = 100 kilometers/hour

There are two situations,

No encounter

Then Time required=(400-100)/100=3 hours

Already met

Then time needed=(40100)/100=5 hours

10. A drives 9 kilometers per hour, and B drives 7 kilometers per hour. Two people are traveling in opposite directions at the same time in two places 6 kilometers apart. How many hours later will they be 150 kilometers apart?

Solution: sum of speeds = 9 + 7 = 16 kilometers per hour

Then after (150-6)/16=144/16=9 hours, the distance is 150 kilometers

12. A project alone takes 10 days to complete, B alone takes 15 days, and team C needs 20 days, 3 teams worked together, Team A left due to something, and it took *** six days. How many days did Team A actually work?

Explanation: The sum of the work efficiency of B and C = 1/ 15+1/20=7/60

B and C both do 6 days, completing 7/60×6=7/10

A completes all 1-7/10= 3/10

Then A actually worked (3/10)/(1/10) = 3 days

12. To process a part, A needs 4 hours and B needs 2.5 hours, C takes 5 hours.

There are now 187 parts that need to be processed. If it takes three people the same amount of time to complete, how many parts should each process?

Solution: A, B, and C need 1/4 hour, 2/5 hour, and 1/5 hour to process one part respectively

Then the completion time = 187/(1/4+ 2/5+1/5)=187/0.85=220 hours

Then A processes 1/4×220=55 pieces

B processes 2/5×220=88 pieces

C processes 1/5 × 220 = 44 pieces

13. For a project, A will first do 5/1, and then the two teams will cooperate, and it will take another 16 days. Finish. It is known that the work efficiency ratio of Team A and Team B is 2:3. How many days does it take for Team A and Team B to complete the project independently?

Solution: The sum of the work efficiency of A and B = (1-1/5)/16= (4/5)/16=1/20

The work efficiency of A = 1/ 20×2/(2+3)=1/50

B’s work efficiency=1/20-1/50=3/100

Then A alone needs 1/ (1/50) = 50 days

B alone needs 1/(3/100) = 100/3 days = 33 and 1/33 days

14. A project , it takes 25 days for Team A to do it alone with 20 people. If it takes 20 days to complete, how many more people need to be added?

Solution: Treat each person’s workload as unit 1

An additional 1×25×20/(1×20)-20=25-20=5 people needs to be added< /p>

15. A works on a project for 3 days first, and then B joins in. 1/3 of the project is completed after 4 days, and 3/4 of the project is completed after 10 days. A is transferred away due to business, leaving B to do all the rest. How many days did one *** last?

Solution: According to the meaning of the question

A and B started to cooperate to complete 1/3 in 4 days, and then completed 3/4 in 10 days

So the cooperation between A and B is 10- 4=6 days to complete 3/4-1/3=5/12

So the sum of A and B’s work efficiency = (5/12)/6=5/72

Then A B’s work efficiency=(1/3-5/72×4)/3=(1/3-5/18)/3=1/54

B’s work efficiency=5/72-1 /54=11/216

Then B completes the rest (1-3/4)/(11/216)=54/11 days

Do it in one day 3+154/11=17 and 10/11 days

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