Downstream distance in fixed time from upstream speed and current: A man rows upstream 32 km in 4 h. If the current is 2 km/h, how far can he go downstream in 6 h?

Introduction / Context:From the upstream speed and the stream speed, we can compute the still-water speed. Once u is known, downstream speed u + v gives distance over the required time.

Given Data / Assumptions:

• Upstream distance/time: 32 km in 4 h ⇒ upstream speed = 8 km/h.
• Stream speed v = 2 km/h.
• Let u be still-water speed.

Concept / Approach:u − v = 8 ⇒ u = 10. Then downstream speed = u + v.

Step-by-Step Solution:u − v = 8 ⇒ u = 8 + 2 = 10 km/h.Downstream speed = 10 + 2 = 12 km/h.Distance in 6 h = 12 * 6 = 72 km.

Verification / Alternative check:Average of up and down equals 10; with v = 2 we get up 8 and down 12, consistent.

Why Other Options Are Wrong:70 and 64 use wrong speeds; 81 assumes 13.5 km/h; 60 assumes 10 km/h downstream.

Common Pitfalls:Using upstream speed directly for downstream distance; subtracting v instead of adding for downstream.

Final Answer:72 km