Recover still-water speed from equal-time trips: A man rows downstream 60 km in 4 h and upstream 36 km in 4 h. What is his still-water speed?

Introduction / Context:
Equal times give direct speeds: downstream distance per hour and upstream distance per hour. Averaging these speeds yields the still-water speed because the current cancels out in the average.

Given Data / Assumptions:

• Downstream speed = 60/4 = 15 km/h.
• Upstream speed = 36/4 = 9 km/h.
• Let u be still-water speed.

Concept / Approach:
u = (down + up)/2; v = (down − up)/2 for reference.

Step-by-Step Solution:
u = (15 + 9) / 2 = 12 km/h.v = (15 − 9) / 2 = 3 km/h (current).

Verification / Alternative check:
Compose to check: u + v = 12 + 3 = 15 (down), u − v = 12 − 3 = 9 (up), matching the data.

Why Other Options Are Wrong:
15 and 8 are individual directional speeds; 16 and 10.5 result from incorrect averaging.

Common Pitfalls:
Averaging distances instead of speeds; forgetting equal times were used to infer speeds.

Final Answer:
12 km/h