A motorboat can travel at 10 km/h in still water. It goes 91 km downstream and returns 91 km upstream to the same place in a total of 20 hours. Find the rate of flow of the river (current speed in km/h).

Question

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

Accepted Answer

Introduction / Context:With still-water speed and total time over symmetric downstream/upstream distances, the current can be solved from a single rational equation. Given Data / Assumptions: b = 10 km/h Distance each way = 91 km Total time = 20 h Let current be c Concept / Approach:Solve 91/(b + c) + 91/(b − c) = 20 for c (0 < c < b). Step-by-Step Solution: 91/(10 + c) + 91/(10 − c) = 2091 * ( (10 − c) + (10 + c) ) / (100 − c^2) = 20 ⇒ 91 * 20 / (100 − c^2) = 201820 / (100 − c^2) = 20 ⇒ 100 − c^2 = 91 ⇒ c^2 = 9 ⇒ c = 3 km/h Verification / Alternative check:Downstream 91/(13) = 7 h; upstream 91/7 = 13 h; total = 20 h, consistent. Why Other Options Are Wrong:2, 4, 5 do not satisfy the sum-of-times equation with b = 10 km/h over 91 km each way. Common Pitfalls:Trying to average the two leg speeds directly; always sum times for unequal speeds over fixed distances. Final Answer:3 km/h.

A motorboat can travel at 10 km/h in still water. It goes 91 km downstream and returns 91 km upstream to the same place in a total of 20 hours. Find the rate of flow of the river (current speed in km/h).

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