If a man rows 6 km downstream in 3 hours and 2 km upstream in 2 hours, then…

Concept: For a boat moving in a stream, if b is the boat's speed in still water and s is the stream's speed, then downstream speed = b + s and upstream speed = b − s. Adding these two equations shows that b = (downstream speed + upstream speed) ÷ 2 — the still-water speed is always the average of the downstream and upstream speeds.

1. Downstream speed = distance ÷ time = 6 km ÷ 3 h = 2 km/h.

2. Upstream speed = distance ÷ time = 2 km ÷ 2 h = 1 km/h.

3. Still-water speed = (downstream speed + upstream speed) ÷ 2 = (2 + 1) ÷ 2 = 1.5 km/h.

4. Time to cover 9 km in still water = distance ÷ speed = 9 km ÷ 1.5 km/h = 6 hours.

Cross-check: speed × time should return the distance, and 1.5 km/h × 6 h = 9 km, which matches the target distance exactly — confirming the still-water speed and the time are consistent.

So the boat takes 6 hours to cover 9 km in still water.