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).

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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.

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).

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