A man can row a boat upstream at 12 km/h and downstream at 18 km/h. What is his rowing speed (in km/h) in still water?

Introduction / Context:
This is another classical upstream–downstream question, where you are asked to find the boatman's own rowing speed in still water. You are given effective speeds in both directions.

Given Data / Assumptions:
• Upstream speed = 12 km/h.• Downstream speed = 18 km/h.• Let speed in still water be u km/h.• Let stream speed be v km/h.

Concept / Approach:
The upstream and downstream speeds are related to u and v as: upstream = u − v, downstream = u + v. Adding these two equations eliminates v and directly gives 2u. So the speed in still water is simply the average of upstream and downstream speeds.

Step-by-Step Solution:
Step 1: Write equations: u − v = 12 and u + v = 18.Step 2: Add the equations: (u − v) + (u + v) = 12 + 18.Step 3: This simplifies to 2u = 30.Step 4: Therefore, u = 30 ÷ 2 = 15 km/h.

Verification / Alternative check:
If u = 15, then v can be found from u + v = 18 ⇒ v = 3 km/h. Check upstream: u − v = 15 − 3 = 12 km/h, which matches the given upstream speed. Both directions are consistent.

Why Other Options Are Wrong:
5 km/hr or 3 km/hr: These values are closer to the speed of the stream than to the boat's own speed.10 km/hr: This is less than both upstream and downstream speeds, which is impossible for the boat's still-water speed.

Common Pitfalls:
Sometimes students mistakenly think the still-water speed is the difference or half the difference of the given speeds. Remember: still-water speed = (upstream + downstream) ÷ 2, and stream speed = (downstream − upstream) ÷ 2.

Final Answer:
The man's rowing speed in still water is 15 km/h.