Boats and Streams – Upstream time is twice downstream time: A person rows at 7.5 km/h in still water. For a fixed distance, rowing upstream takes twice as long as rowing downstream. What is the speed of the stream?

Introduction / Context:
In boats-and-streams, still-water speed and stream speed combine linearly: downstream = u + v and upstream = u − v. When times differ by a given factor for the same distance, we set up a ratio of speeds using time = distance / speed.

Given Data / Assumptions:

• Still-water rowing speed u = 7.5 km/h.
• Upstream time is twice downstream time for the same distance.

Concept / Approach:
Let speeds be S_up = u − v and S_down = u + v. Since time is inversely proportional to speed for fixed distance, 1/(u − v) = 2 * 1/(u + v). Rearranging gives a linear equation in v.

Step-by-Step Solution:
u + v = 2(u − v).u + v = 2u − 2v ⇒ 3v = u ⇒ v = u / 3.Therefore v = 7.5 / 3 = 2.5 km/h.

Verification / Alternative check:
Speeds become S_down = 10 km/h and S_up = 5 km/h, so upstream time is indeed double downstream time for any fixed distance.

Why Other Options Are Wrong:
2.0, 2.2, 2.7, 3.0 km/h do not satisfy the 2:1 time ratio when combined with u = 7.5 km/h.

Common Pitfalls:
Using time ratio directly on u without accounting for stream v, or mixing the direction for addition and subtraction.

Final Answer:
2.5 km/h