A river flows at 4 km/h. A rower goes downstream from the start to a turning point and then rows back upstream to the start. The total distance covered is 42 km (so each leg is 21 km). The upstream journey takes 2 hours more than the downstream.

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

Accepted Answer

Introduction / Context:This round-trip problem provides different times for equal distances in opposite directions, along with a known current. By writing the two leg times and using the given 2-hour difference, we can solve for the still-water speed using a single equation in v. Given Data / Assumptions: Current speed c = 4 km/h. Each leg distance D = 21 km (since total is 42 km). Let v be still-water speed. Upstream time − downstream time = 2 h. Concept / Approach:Downstream time t1 = D/(v + c). Upstream time t2 = D/(v − c). The condition is t2 = t1 + 2. Substitute D and c and solve for v. Step-by-Step Solution: 21/(v − 4) = 21/(v + 4) + 2.Bring terms: 21/(v − 4) − 21/(v + 4) = 2.Left side = 21[(v + 4) − (v − 4)]/((v − 4)(v + 4)) = 168/(v^2 − 16).So 168/(v^2 − 16) = 2 ⇒ v^2 − 16 = 84 ⇒ v^2 = 100 ⇒ v = 10 km/h (positive root). Verification / Alternative check:Downstream speed 14 ⇒ t1 = 21/14 = 1.5 h. Upstream speed 6 ⇒ t2 = 21/6 = 3.5 h. Difference = 2 h matches the condition. Why Other Options Are Wrong:12, 9, 8 km/h do not satisfy the derived equation and will not create a 2-hour time gap over 21 km per leg with c = 4. Common Pitfalls:Using total distance in each time or forgetting to split 42 km into two equal legs. Final Answer:10 km/h

A river flows at 4 km/h. A rower goes downstream from the start to a turning point and then rows back upstream to the start. The total distance covered is 42 km (so each leg is 21 km). The upstream journey takes 2 hours more than the downstream journey. Find the rower speed in still water (km/h).

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