In still water a rower has speed 7.5 km/h. It takes twice as long to row upstream a given distance as it takes to row the same distance downstream. What is the stream speed?

Introduction / Context:
Rowing problems use effective speeds: downstream uses still water speed plus current, and upstream uses still water speed minus current. A time ratio condition lets us relate these speeds to find the current speed.

Given Data / Assumptions:

• Still water speed u = 7.5 km/h.
• Let current speed be v.
• Time upstream is twice the time downstream for the same distance.

Concept / Approach:
Time is proportional to 1 / speed for equal distances. If T_up = 2 * T_down, then 1 / (u - v) = 2 / (u + v). Solve for v.

Step-by-Step Solution:

Verification / Alternative check:
Downstream speed = 7.5 + 2.5 = 10 km/h. Upstream speed = 7.5 - 2.5 = 5 km/h. Time ratio for same distance is 1/5 vs 1/10, i.e., upstream time is exactly double downstream time.

Why Other Options Are Wrong:
2.0, 2.2, and 2.7 km/h do not satisfy 1/(7.5 - v) = 2/(7.5 + v) when checked numerically.

Common Pitfalls:
Using speed ratio instead of time ratio or accidentally adding speeds for upstream.

Final Answer:
2.5 km/h