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).

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:

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