A man rows at 9 1/3 km/h in still water. He takes three times as long to row a fixed distance upstream as he takes to row the same distance downstream. Find the speed of the current (in km/h).

Introduction / Context:Time ratio information links upstream and downstream speeds via reciprocal relations. If upstream time is 3 times downstream time for equal distances, the upstream speed must be one-third of the downstream speed.

Given Data / Assumptions:

• Still-water speed b = 9 1/3 km/h = 28/3 km/h
• Let current speed be c
• Upstream speed vu = b − c; downstream speed vd = b + c
• Given t_up = 3 * t_down ⇒ vu = (1/3) vd

Concept / Approach:Use b − c = (1/3)(b + c) to relate b and c and solve for c.

Step-by-Step Solution:

Verification / Alternative check:vd = b + c = (28/3) + (14/3) = 42/3 = 14; vu = b − c = (28/3) − (14/3) = 14/3. Then t_up/t_down = (distance/vu)/(distance/vd) = vd/vu = 14 / (14/3) = 3, matching the condition.

Why Other Options Are Wrong:Other fractions do not equal b/2 when b = 28/3, and they break the 3:1 time ratio.

Common Pitfalls:Inverting the 3:1 relationship improperly or averaging speeds instead of using the reciprocal time-speed relation for equal distances.

Final Answer:14/3 km/hr.