A steamer goes from one port to another downstream in 4 hours and returns upstream in 5 hours. If the stream speed is 2 km/h, find the distance between the two ports (in km).

Introduction / Context:When upstream and downstream times are given for the same distance with a known current, we can deduce the still-water speed and then compute the distance.

Given Data / Assumptions:

• Downstream time = 4 h, upstream time = 5 h
• Stream c = 2 km/h
• Let still-water speed be b; distance be D

Concept / Approach:D = 4(b + 2) and D = 5(b − 2). Equate to solve for b, then compute D.

Step-by-Step Solution:

Verification / Alternative check:Upstream speed b − c = 16 km/h ⇒ time = 80/16 = 5 h; downstream speed b + c = 20 km/h ⇒ time = 80/20 = 4 h, as given.

Why Other Options Are Wrong:50, 60, 70 do not satisfy both time conditions with c = 2 km/h.

Common Pitfalls:Using average of 4 and 5 hours or averaging speeds; equate distances via b ± c instead.

Final Answer:80 km.