A boatman rows 1 km in 5 minutes along the stream (downstream), and 6 km in 1 hour against the stream (upstream). Find the speed of the stream (in km/h).
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A3 km/h
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B6 km/h
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C10 km/h
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D12 km/h
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ENone of these
Answer
Correct Answer: 3 km/h
Explanation
Introduction / Context:This question gives downstream and upstream travel rates to deduce the current speed. Converting times to hours is essential.
Given Data / Assumptions:
- Downstream: 1 km in 5 min ⇒ 5 min = 5/60 h = 1/12 h.
- Upstream: 6 km in 1 h.
- Downstream speed vd and upstream speed vu are in km/h.
Concept / Approach:Compute vd and vu, then use vd = b + c and vu = b − c to find current c = (vd − vu)/2.
Step-by-Step Solution:
vd = distance/time = 1 / (1/12) = 12 km/hvu = 6 / 1 = 6 km/hc = (vd − vu)/2 = (12 − 6)/2 = 3 km/hVerification / Alternative check:Then b = (vd + vu)/2 = (12 + 6)/2 = 9 km/h; check: b + c = 12 and b − c = 6, consistent with data.
Why Other Options Are Wrong:6, 10, 12 km/h do not satisfy both downstream and upstream relations simultaneously when combined with a single boat speed b.
Common Pitfalls:Forgetting to convert 5 minutes to hours; misapplying average vs half-difference. Average gives boat speed, not current speed.
Final Answer:3 km/h.