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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
Places A and B are $100\text{ km}$ apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in $5$ hours. If they travel towards each other, they meet in $1$ hour. What are the speeds of the two cars?
Step-by-Step Solution
Key Concept: Let speeds be $x$ and $y$ ($x > y$). Relative speed same direction: $x - y = 100/5 = 20$. Relative speed opposite direction: $x + y = 100/1 = 100$. Add: $2x = 120 \Rightarrow x = 60, y = 40\text{ km/h}$.
Equations: (1) $x - y = 20$, (2) $x + y = 100$. [1.0 Mark] Add equations: $2x = 120 \Rightarrow x = 60\text{ km/h}$. [1.0 Mark] $y = 100 - 60 = 40\text{ km/h}$. Speeds are $60\text{ km/h}$ and $40\text{ km/h}$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Forming relative speed equations: 1.0 Mark Solving $x = 60\text{ km/h}$: 1.0 Mark Solving $y = 40\text{ km/h}$: 1.0 Mark
Correct Answer:
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