The current of a stream runs at 1 km/h. A motorboat goes 35 km upstream and returns 35 km downstream to the start in a total of 12 hours. Find the boat’s speed in still water (in km/h).

Introduction / Context:
Round-trip time with a known current allows solving for the still-water speed b using the sum of upstream and downstream times over equal distances.

Given Data / Assumptions:

• Current c = 1 km/h
• Distance each way = 35 km
• Total time = 12 h
• Upstream speed = b − 1; downstream speed = b + 1

Concept / Approach:
Set 35/(b − 1) + 35/(b + 1) = 12 and solve the quadratic for b > 0.

Step-by-Step Solution:

Verification / Alternative check:
Upstream speed 5 km/h ⇒ time 35/5 = 7 h; downstream speed 7 km/h ⇒ time 35/7 = 5 h; total = 12 h.

Why Other Options Are Wrong:
7, 8, 8.5 do not satisfy the time equation for both legs with c = 1 km/h.

Common Pitfalls:
Forgetting to set up the rational sum correctly or trying to average speeds arithmetically; the correct method sums times.

Final Answer:
6 km/hr.