A steamer goes downstream between two ports in 4 hours and the same distance upstream in 5 hours. If stream speed is 2 km/h, what is the distance between the ports (in km)?

Introduction / Context:
This problem combines upstream and downstream travel times with a known stream speed to find the distance between ports. It uses the standard effective speed idea for boats in streams.

Given Data / Assumptions:

• Downstream time = 4 h; upstream time = 5 h.
• Stream speed v = 2 km/h.
• Let still water speed be u km/h and distance be D km.

Concept / Approach:
Downstream speed = u + v; upstream speed = u - v. Hence D = (u + v) * 4 and D = (u - v) * 5. Equate to solve u, then compute D.

Step-by-Step Solution:

Verification / Alternative check:
Upstream speed = 16 km/h. Time upstream = 80 / 16 = 5 h, matching the given time, so the result is consistent.

Why Other Options Are Wrong:
50, 60, and 70 km do not satisfy both time equations simultaneously when checked against stream speed 2 km/h.

Common Pitfalls:
Mistakenly using an average of speeds or averaging times, instead of using effective speeds with equations.

Final Answer:
80 km