Find current speed from unequal up/down distances and equal times: A man rows upstream 16 km in 5 h and downstream 27 km in 5 h. What is the velocity of the current?

Introduction / Context:When times are equal but distances differ, the given distances per equal time directly give the upstream and downstream speeds. With those two, we compute the still-water speed and stream speed using simple averages.

Given Data / Assumptions:

• Upstream: 16 km in 5 h ⇒ 3.2 km/h.
• Downstream: 27 km in 5 h ⇒ 5.4 km/h.
• Let u be boat speed in still water and v the current speed.

Concept / Approach:Use identities: upstream = u − v, downstream = u + v. Then u = (down + up)/2 and v = (down − up)/2.

Step-by-Step Solution:u − v = 3.2, u + v = 5.4.u = (3.2 + 5.4) / 2 = 4.3 km/h.v = (5.4 − 3.2) / 2 = 1.1 km/h.

Verification / Alternative check:Plug back: downstream 4.3 + 1.1 = 5.4, upstream 4.3 − 1.1 = 3.2, which match the observed rates.

Why Other Options Are Wrong:2 or 2.1 overshoot the half-difference; 1.8 is the full difference minus an error; “None” is needless since 1.1 matches exactly.

Common Pitfalls:Using average of distances instead of speeds; mixing minutes and hours; forgetting to divide the difference by 2.

Final Answer:1.1 km/hr