Distance ÷ (speed sum) = meeting time
Meeting time × (speed sum) = distance
Speed of a = distance ÷ meeting time-speed of b
The following three problems are the most basic types and can be solved by equations or arithmetic. Apply the above formula.
First, basic exercises
(1) Two trains A and B run in opposite directions from two places 700 kilometers apart at the same time. The speed of train A is 85 kilometers per hour, and that of train B is 90 kilometers per hour. How many hours do the two trains meet?
Two trains leave from two stations in opposite directions at the same time. Car A travels at a speed of 48 kilometers per hour, and car B travels at a speed of 78 kilometers per hour. Two and a half hours later, two trains met. How many kilometers is the railway between the two stations?
(3) The two trains, A and B, run in opposite directions from two places 988 kilometers apart at the same time, and meet after 5.2 hours. The speed of train A is 93 kilometers per hour, and that of train B is how many kilometers per hour?
Second, comprehensive exercises.
"Go or open" is only a basic carrier of the encounter problem, and some exercises seem to have nothing to do with "go or open", but their essence is also the encounter problem. In fact, it is also a meeting problem for two people to finish a job together.
Sometimes you will encounter sentences such as "there is still a distance of so-and-so kilometers" or "there is still some unfinished work" At this time, you have to subtract this unfinished work from the total amount of work.
Please look at the following questions.
(1) The master and the apprentice processed 520 parts together. The master processes 30 parts per hour and the apprentice processes 20 parts per hour. How many hours later, there are still 70 parts to be processed?
(2) Team A and Team B dig a canal together. Team a digs from east to west, digging 75 meters every day; Team B dug from west to east, digging 5 meters less than Team A every day, and the two teams cooperated for 8 days to dig well. How long is this canal?
(3) Two ships A and B set out from two places 654 kilometers apart, and eight hours later, the two ships were still 22 kilometers apart. It is known that ship B travels 42 kilometers per hour, and how many kilometers does ship A travel per hour?
Third, improve the exercises.
Some exercises are relatively difficult, and some are not given directly. It is necessary to find the relationship between unknown conditions and known conditions.
Please look at the following questions.
(1) A car and a bicycle set off from Party A and Party B, which are 172.5km away, and walked in opposite directions. Three hours later, two cars met. It is known that cars travel 3 1.5km more per hour than bicycles. What are the speeds of cars and bicycles? You can use an equation, set a speed as x, then use a formula containing x to represent another speed, and then list the equations according to the equivalence relationship.
(2) The distance between the two places is 270 kilometers. Two trains, A and B, started from two places at the same time and met four hours later. It is known that the speed of train A is 1.5 times that of train B, and how many kilometers are required for the speed of train A and train B respectively? We can use the equation to set one of the speeds as X, then use the formula containing X to represent the other speed, and then list the equation according to the equivalence relationship.
(3) The distance between City A and City B is 680 kilometers. The ordinary bus from city A to city B travels 60 kilometers per hour. Two hours later, the express from B to A was 80 kilometers per hour. How many hours after the express train left, the two cars met? The ordinary bus takes 2 hours first, and the two cars have different distances. What should I do?
(4) The two sisters walked 770 meters from home to Children's Palace at the same time. My sister walks 60 meters per minute, and my sister rides her bike to the Children's Palace at a speed of 160 meters per minute and returns immediately. She met her sister on the road. Then my sister walked for a few minutes. When two people met, how far did a * * * go?
(5) Xiaoming and Xiaohua set out from A and B at the same time and walked in opposite directions. Xiaoming walks 60 meters every minute, Xiaohua rides a bike 190 meters every minute, and they meet at a distance of 650 meters in a few minutes? Meeting at a distance of 650 meters from the midpoint shows how many meters Xiaohua has walked more than Xiaoming. This is their distance difference. Distance difference ÷ (speed difference) = * * peer walking time
(6)A and B are 300 kilometers apart, and two cars start from both places at the same time and drive in opposite directions. They returned immediately after arriving at their destination and met for the second time eight hours later. It is known that car A travels 45 kilometers per hour. How many kilometers does bus B travel per hour? The second encounter problem, draw a picture to see, when two people meet for the second time, how many times has a * * * gone?