The current of a stream runs at 1 km/h. A motorboat goes 35 km upstream and returns 35 km downstream to the start in a total of 12 hours. Find the boat’s speed in still water (in km/h).
Aptitude
Boats and Streams
Difficulty: Medium
Choose an option
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A6 km/hr
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B7 km/hr
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C8.5 km/hr
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D8 km/hr
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ENone of these
Answer
Correct Answer: 6 km/hr
Explanation
Introduction / Context:Round-trip time with a known current allows solving for the still-water speed b using the sum of upstream and downstream times over equal distances.
Given Data / Assumptions:
- Current c = 1 km/h
- Distance each way = 35 km
- Total time = 12 h
- Upstream speed = b − 1; downstream speed = b + 1
Concept / Approach:Set 35/(b − 1) + 35/(b + 1) = 12 and solve the quadratic for b > 0.
Step-by-Step Solution:
35/(b − 1) + 35/(b + 1) = 1235 * ( (b + 1) + (b − 1) ) / (b^2 − 1) = 12 ⇒ 35 * (2b) = 12(b^2 − 1)70b = 12b^2 − 12 ⇒ 12b^2 − 70b − 12 = 0Solve ⇒ b = 6 km/h (reject negative root)Verification / Alternative check:Upstream speed 5 km/h ⇒ time 35/5 = 7 h; downstream speed 7 km/h ⇒ time 35/7 = 5 h; total = 12 h.
Why Other Options Are Wrong:7, 8, 8.5 do not satisfy the time equation for both legs with c = 1 km/h.
Common Pitfalls:Forgetting to set up the rational sum correctly or trying to average speeds arithmetically; the correct method sums times.
Final Answer:6 km/hr.