A man can row at 7.5 km/h in still water. The river current flows at 1.5 km/h. He rows from the start to a place and returns to the start in a total of 50 minutes. How far is the place from the start (one-way distance, in km)?

Introduction / Context:Round-trip time with different downstream and upstream speeds can be used to deduce the one-way distance. This is a straightforward harmonic-like setup using v ± c and a fixed total time.

Given Data / Assumptions:

• v = 7.5 km/h (still water).
• c = 1.5 km/h (current).
• Total time T = 50 min = 5/6 h.
• Let one-way distance be d (km).

Concept / Approach:Downstream speed = v + c = 9 km/h. Upstream speed = v − c = 6 km/h. Total time = d/9 + d/6. Set equal to 5/6 and solve for d.

Step-by-Step Solution:

Verification / Alternative check:Downstream time = 3/9 = 1/3 h = 20 min; upstream time = 3/6 = 1/2 h = 30 min; total = 50 min as required.

Why Other Options Are Wrong:4, 1, or 2 km do not sum to 50 min using speeds 9 and 6 km/h.

Common Pitfalls:Using an average speed over the entire loop; correct method is to add segment times with their respective speeds.

Final Answer:3 km