Venkat can row a boat in still water at the speed of 12 km/h. He ferries tourists 15 km upstream and 18 km downstream in 3 hours. Find the speed of the stream.
Generated by claude-sonnet-4-6 · 2026-06-15 10:35 · grounding rag
Model Answer
Let the speed of the stream = x km/h
- Speed upstream = (12 − x) km/h
- Speed downstream = (12 + x) km/h
Forming the equation:
Time = Distance ÷ Speed
$$\frac{15}{12 - x} + \frac{18}{12 + x} = 3$$
Solving:
$$15(12 + x) + 18(12 - x) = 3(12 - x)(12 + x)$$
$$180 + 15x + 216 - 18x = 3(144 - x^2)$$
$$396 - 3x = 432 - 3x^2$$
$$3x^2 - 3x - 36 = 0$$
$$x^2 - x - 12 = 0$$
$$(x - 4)(x + 3) = 0$$
$$x = 4 \quad \text{or} \quad x = -3$$
Since speed cannot be negative, x = −3 is rejected.
∴ Speed of the stream = 4 km/h
Verification: Upstream speed = 8 km/h, Downstream speed = 16 km/h.
Time = 15/8 + 18/16 = 15/8 + 9/8 = 24/8 = 3 h ✓
Source: Chapter 3, Pair of Linear Equations in Two Variables
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Explanation
- The key step is setting up the time equation using Time = Distance/Speed for both upstream and downstream journeys.
- After cross-multiplying, the equation simplifies to a quadratic — factorise and reject the negative root since speed is always positive.
- Always include the verification step; it carries marks in CBSE board exams.
- Examiners award marks at each stage: forming the equation (1 mark), simplification (1 mark), factorisation (1 mark), correct root with reason for rejection (1 mark), and verification (1 mark).