The intersection of two people's distance graphs represents the time and place where they meet.
Example ①
A and B walk toward each other at the same time from points 12 km apart. A walks at 3 km/h, and B walks at 5 km/h. After how many hours will they meet?
Answer: A's distance from A: y=3x. B's distance from A: y=12−5x. At the intersection: 3x=12−5x→8x=12→x=1.5 hours later. 1.5 hours later
A and B walk toward each other at the same time from points 12 km apart. A walks at 3 km/h, and B walks at 5 km/h. After how many hours will they meet?
Answer: A's distance from A: y=3x. B's distance from A: y=12−5x. At the intersection: 3x=12−5x→8x=12→x=1.5 hours later. 1.5 hours later
Key Points
- Same direction → pursuit (calculate using the speed at which the difference decreases).
- Opposite directions → meeting (the distance decreases at their combined speed).
- The x-coordinate of the intersection = the time they meet.
Practice Problems
- A and B walk toward each other at the same time from points 20 km apart. A walks at 4 km/h, and B walks at 6 km/h. After how many hours will they meet?
Answer and Explanation
- Answer: 2 hours later. 4x+6x=20→10x=20→x=2.