Now let's solve a few problems about moving in the opposite direction:
1. The distance between Party A and Party B is 2 1 km. If they go in the opposite direction, they will meet in 1 hour. If they go in the same direction, Party B will catch up with Party A within 7 hours. How many kilometers do Party A and Party B walk every hour?
2. The speed ratio of Party A and Party B is 13: 1 1. If Party A and Party B go in opposite directions at the same time and meet in 0.5 hours, if they go in the same direction, how many hours will it take for Party A to catch up with Party B?
Answer: 1. When they met, A and B walked 2 1 km, indicating that the speed sum of A and B was 2 1 km. And they travel in the same direction, the catching-up distance is 2 1 km and the catching-up time is 7 hours, so the speed difference between them is 2 1÷7=3 (km).
According to the solution of sum-difference problem, large number = (sum+difference) ÷2, because when B lags behind A, B can catch up with A, which means that the speed of B is a large number, so the speed of B is (2 1+3)÷2= 12 (km).
Then the speed of A is 2 1- 12=9 (km) or 12-3=9 (km).
When they meet within 2.0.5 hours, Party A and Party B walk 1 hour * * 24 copies13+1=, and the actual distance * * * after walking for half an hour is the distance between them. The difference between them is 24×0.5= 12 copies.
Then if A chases B 13- 1 1=2 copies per hour, then A needs 12÷2=6 (hours) to catch up with B.
In addition, this kind of problem is often called "occasional problem". The trick is to fully understand the meaning of the problem and grasp the quantitative relationship.
To fully understand the meaning of the question, it is necessary to read the question carefully and make a clear investigation of it:
Whether the two cars leave at the same time or successively;
How long did you drive? Did you stop over?
The two cars met, or haven't met, or have met;
How far is the distance between the two places, or the distance between the two cars.
Fully understand the meaning of the question, including the requirements of the question, whether to ask for a meeting time, the distance between the two places, or the speed, etc.
Grasp the quantitative relationship, that is, according to the quantitative relationship:
"speed and x meet time = distance",
Two other quantitative relationships are obtained:
"Distance ÷ speed and = meeting time",
Distance ÷ meeting time = speed and.
Starting with the problem, draw a line segment diagram, analyze the relationship between the known conditions and the required problems, and choose the corresponding quantitative relationship.