A boat travels upstream from B to A and then downstream from A back to B in a total of 3 hours. If the boat’s still-water speed is 9 km/h and the current is 3 km/h, find the distance between A and B (in km).

Introduction / Context:Round-trip problems use different leg speeds. Knowing still-water speed and current lets us compute each leg's speed and then the distance from total time.

Given Data / Assumptions:

• b = 9 km/h (still water)
• c = 3 km/h (current)
• Upstream speed vu = b − c = 6 km/h
• Downstream speed vd = b + c = 12 km/h
• Total time = 3 h; one-way distance = d km

Concept / Approach:Total time = d/vu + d/vd. Solve for d.

Step-by-Step Solution:

Verification / Alternative check:Upstream time = 12/6 = 2 h; downstream time = 12/12 = 1 h; total = 3 h, matches.

Why Other Options Are Wrong:4, 6, 8 give totals smaller than 3 h; they do not satisfy the time equation.

Common Pitfalls:Using the arithmetic average of speeds to find time. Average speed is not applicable across legs with different speeds unless weighted by time/distance correctly.

Final Answer:12 km.