For example, suppose two people, A and B, start from two points 400 meters apart and walk along the same straight line. The speed of A is 60m/min, and that of B is 40m/min. We need to find out where they will meet and how far they have gone.
Let's set t as the time required for two people to meet (unit: minutes), so there are two equations: A walks 60t (speed times time) and B walks 40t. Because they started from two points 400 meters apart, when they met, the total distance they walked should be equal to 400 meters. So we get the equation: 60t+40t=400. Solving this linear equation, we get: t=4 (minutes).
So, A and B will meet in 4 minutes. At this time, A will walk 60×4=240 (meters) and B will walk 40×4= 160 (meters). This is the distance they walked when they met.
This example shows how the one-dimensional linear equation can help us solve the problem of meeting. By establishing equations, we can find the time required for meeting and the distance traveled by each object.
Skills to solve the encounter problem of linear equations with one variable;
1. Understand the background of the problem: First, understand the background of the problem and the objects or people involved. Determine the initial distance and relative speed between them.
2. Establish an equation: According to the description of the problem, we can establish a linear equation and find out the time of meeting. Equations usually relate to the relationship between speed, time and distance.
3. Solving the equation: Solve this one-dimensional linear equation and find out the time to meet the needs. This usually includes replacing known values and solving unknown values.
4. Find the intersection point: According to the solved time, we can calculate the distance traveled by two objects when they meet, so as to determine their intersection point on a straight line.
5. Verify the answer: We need to verify whether the answer conforms to the description of the question. This usually involves recalculating and checking all relevant values.