Boats and Streams – Find port-to-port distance from up/down times and stream speed: A steamer covers a downstream trip in 4 hours and the same route upstream in 5 hours. If the stream speed is 2 km/h, what is the distance between the two ports?

Introduction / Context:
This uses the standard downstream and upstream speed relations with a known stream speed. With both travel times given, we can solve for still-water speed and then compute the distance directly from either leg.

Given Data / Assumptions:

• Downstream time = 4 h; upstream time = 5 h.
• Stream speed v = 2 km/h; still-water speed u is unknown.
• Distance D is the same each way.

Concept / Approach:
Downstream speed = u + v; upstream speed = u − v. Thus D = (u + 2)*4 = (u − 2)*5. Solve for u, then compute D.

Step-by-Step Solution:
4u + 8 = 5u − 10 ⇒ u = 18 km/h.Distance D = (u + 2)*4 = 20 * 4 = 80 km.

Verification / Alternative check:
Using upstream: (u − 2)*5 = 16 * 5 = 80 km, consistent with downstream calculation.

Why Other Options Are Wrong:
60, 70, 72, and 50 km fail to satisfy both leg equations simultaneously with stream speed 2 km/h.

Common Pitfalls:
Confusing which leg is faster or failing to use the same distance for both directions.

Final Answer:
80 km