A boat takes 9 hours to travel a distance upstream and 3 hours to travel the same distance downstream. If the boat’s still-water speed is 4 km/h, find the speed of the stream (in km/h).

Introduction / Context:
Equal distances with different times specify upstream and downstream effective speeds. Combine with the still-water speed identity to find the current.

Given Data / Assumptions:

• Still-water speed b = 4 km/h
• Same distance d for upstream and downstream
• Upstream time = 9 h ⇒ vu = d/9
• Downstream time = 3 h ⇒ vd = d/3

Concept / Approach:
Use b = (vd + vu)/2 and c = (vd − vu)/2 because vd = b + c and vu = b − c.

Step-by-Step Solution:

Verification / Alternative check:
vu = b − c = 2 km/h ⇒ time upstream = 18/2 = 9 h; vd = b + c = 6 km/h ⇒ time downstream = 18/6 = 3 h; consistent.

Why Other Options Are Wrong:
3, 4, 6 contradict the still-water speed condition when reconstructed.

Common Pitfalls:
Trying to solve directly for speeds without relating them to distance; use the identities for sums and differences.

Final Answer:
2 km/h.