Downstream speed from still-water and upstream speeds: A man rows at 5 km/h in still water. His speed against the current is 3.5 km/h. What is his speed along the current (downstream)?

Introduction / Context:
Problems on boats and streams test the idea of relative speed in running water. The speed of a boat in still water (u) is modified by the stream speed (v): downstream speed is u + v, while upstream speed is u − v. Knowing any two of these lets us find the third.

Given Data / Assumptions:

• Still-water speed u = 5 km/h.
• Upstream speed u − v = 3.5 km/h.
• We assume uniform speeds and straight reach (no turns), and calm conditions.

Concept / Approach:
From u − v we recover v, then compute downstream speed u + v. All arithmetic uses simple addition/subtraction because the stream contributes linearly to the boat’s ground speed.

Step-by-Step Solution:
u − v = 3.5 ⇒ v = u − 3.5 = 5 − 3.5 = 1.5 km/h.Downstream speed = u + v = 5 + 1.5 = 6.5 km/h.

Verification / Alternative check:
Average of downstream and upstream equals still-water speed: ( (u + v) + (u − v) ) / 2 = u. Using 6.5 and 3.5 gives (6.5 + 3.5) / 2 = 5, matching u = 5.

Why Other Options Are Wrong:
8.5 and 6 are not u + v for the found v; 4.25 is neither upstream nor downstream here; 5.5 assumes v = 0.5, which contradicts u − v = 3.5.

Common Pitfalls:
Confusing still-water speed with downstream speed; forgetting that upstream reduces speed by v while downstream increases it by v.

Final Answer:
6.5 km/hr