Question

Swati can row a boat on still water at a speed of 5 km/hr. However, on a given river, it takes her 1 hour more to row the boat 12 km upstream than downstream. One day, Swati rows the boat on this river from X to Y, which is N km upstream from X. Then she rows back to X immediately. If she takes at least 2 hours to complete this round trip, what is the minimum possible value of N?

Accepted Answer

B. Let river speed be $v$ km/hr. Upstream speed = $5 - v$, Downstream speed = $5 + v$. Given: $\frac{12}{5-v} - \frac{12}{5+v} = 1 \implies 12 \left(\frac{2v}{25-v^2}\right) = 1 \implies 24v = 25 - v^2 \implies v^2 + 24v - 25 = 0 \implies v = 1$ km/hr. Upstream speed = 4 km/hr, Downstream speed = 6 km/hr. Round trip time for distance $N$: $T = \frac{N}{4} + \frac{N}{6} = \frac{5N}{12}$. Given $T \ge 2 \implies \frac{5N}{12} \ge 2 \implies N \ge 4.8$ km.

Minimum Distance for Round Boat Trip

Explanation

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