A motorboat makes two trips at the same engine setting: (i) 25 km upstream and 39 km downstream in 8 hours, (ii) 35 km upstream and 52 km downstream in 11 hours. Find the speed of the stream.

Introduction / Context:
When a boat travels upstream and downstream at a fixed engine setting, the still-water speed b and current speed c remain constant. Two mixed trips yield a solvable system for b and c.

Given Data / Assumptions:

• Trip 1 time: 25 km upstream + 39 km downstream in 8 h.
• Trip 2 time: 35 km upstream + 52 km downstream in 11 h.
• Upstream speed = b - c; downstream speed = b + c.

Concept / Approach:
Use time = distance / speed on each leg and sum. This yields two equations in b and c.

Step-by-Step Solution:
25/(b - c) + 39/(b + c) = 8 35/(b - c) + 52/(b + c) = 11 Solve simultaneously to obtain b = 9 km/h and c = 4 km/h.

Verification / Alternative check:
Check Trip 1: 25/5 + 39/13 = 5 + 3 = 8 h. Check Trip 2: 35/5 + 52/13 = 7 + 4 = 11 h. Perfect.

Why Other Options Are Wrong:
2, 3, or 5 km/h do not satisfy both equations simultaneously; they break one of the total-time sums.

Common Pitfalls:
Adding numerators and denominators incorrectly; assuming average of speeds instead of harmonic structure; arithmetic slips when solving rational equations.

Final Answer:
4 km/h