A motorboat travels 35 km upstream and returns 35 km downstream in a total of 12 hours. If the stream runs at 1 km/h, what is the motorboat speed in still water?

Introduction / Context:Round trips on a river involve two effective speeds: upstream (slower) and downstream (faster). Knowing total time and the stream current, we can solve for the still water speed of the boat.

Given Data / Assumptions:

• Upstream distance = 35 km; downstream distance = 35 km.
• Total time = 12 h.
• Stream speed v = 1 km/h.
• Let still water speed be u km/h.

Concept / Approach:Time upstream = 35 / (u - v), and time downstream = 35 / (u + v). Sum equals 12. Solve for u with v = 1.

Step-by-Step Solution:

Verification / Alternative check:Upstream speed = 5 km/h; time upstream = 35 / 5 = 7 h. Downstream speed = 7 km/h; time downstream = 35 / 7 = 5 h. Total = 12 h as required.

Why Other Options Are Wrong:7, 5, and 4 km/h produce totals different from 12 h when substituted into the equation with v = 1.

Common Pitfalls:Adding or averaging speeds directly instead of forming the time equation. Forgetting that upstream uses u - v and downstream uses u + v.

Final Answer:6 km/h