Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.
Generated by claude-sonnet-4-6 · 2026-06-15 10:33 · grounding rag
Model Answer
Let the speeds of the two persons be x km/h and y km/h (x > y).
Setting up equations:
When walking towards each other, relative speed = (x + y) km/h.
They meet in 2 hours, covering 16 km:
$$x + y = \frac{16}{2} = 8 \quad \text{...(1)}$$
When walking in the same direction, relative speed = (x − y) km/h.
They meet in 8 hours, covering 16 km:
$$x - y = \frac{16}{8} = 2 \quad \text{...(2)}$$
Solving by elimination:
Adding (1) and (2):
$$2x = 10 \implies x = 5$$
Substituting in (1):
$$5 + y = 8 \implies y = 3$$
∴ The speeds of the two persons are 5 km/h and 3 km/h.
Source: Chapter 3, Pair of Linear Equations in Two Variables
---
Explanation
- The key idea is relative speed: towards each other → add speeds; same direction → subtract speeds.
- Use Distance = Speed × Time to form both equations directly.
- Elimination method (adding/subtracting equations) is the quickest approach here.
- Examiners award marks for: correct equations (1 mark), correct solving (1 mark), correct answer with units (1 mark). Always state the final answer clearly.