Velocity of current from unequal up and down distances: A man rows upstream 16 km and downstream 28 km taking 5 hours each time. What is the velocity of the current?

Introduction / Context:
Here, different distances are covered upstream and downstream but with equal times. This allows direct computation of effective speeds in both directions and then the current speed by halving their difference.

Given Data / Assumptions:

• Upstream distance = 16 km in 5 h ⇒ su
• Downstream distance = 28 km in 5 h ⇒ sd
• Uniform current and straight path

Concept / Approach:
Compute su = 16/5 km/h and sd = 28/5 km/h. Then current speed v = (sd - su)/2. Still water speed u = (sd + su)/2 if needed.

Step-by-Step Solution:

Verification / Alternative check:
u = (5.6 + 3.2)/2 = 4.4 km/h. Then upstream u - v = 3.2 and downstream u + v = 5.6, consistent with the computed rates.

Why Other Options Are Wrong:

• 2.4 km/h equals the full difference sd - su, not the current v.
• 3.6 km/h and 1.8 km/h are not half the speed difference.
• 0.8 km/h is too small and does not reproduce the observed rates.

Common Pitfalls:
Forgetting to halve the difference between effective speeds; mixing km and hours. Always use v = (sd - su)/2 with consistent units.

Final Answer:
1.2 km/h