Finding still water speed from round-trip time: A stream runs at 4 km/h. A boat goes 6 km downstream and returns 6 km upstream to the start in a total of 2 hours. What is the boat's speed in still water?

Introduction / Context:
For a round trip in a current, the total time equals the sum of downstream and upstream times. Using the stream speed, we can set an equation in the unknown still water speed u and solve it.

Given Data / Assumptions:

• Stream speed v = 4 km/h
• Downstream distance = 6 km
• Upstream distance = 6 km
• Total time T = 2 h

Concept / Approach:
Time downstream = 6 / (u + v). Time upstream = 6 / (u - v). Their sum equals 2. Solve for u > v.

Step-by-Step Solution:

Verification / Alternative check:
Downstream speed 12 km/h gives 0.5 h; upstream speed 4 km/h gives 1.5 h; total 2 h, consistent.

Why Other Options Are Wrong:

• 7.5, 6.8, and 6 km/h do not satisfy the time equation.
• 10 km/h yields total time less than 2 h.

Common Pitfalls:
Adding distances and averaging speeds directly. Always sum times with correct effective speeds and solve the resulting equation carefully.

Final Answer:
8 km/h