Upstream speed from downstream speed and stream rate: A swimmer's downstream speed is 11 km/h and the stream's speed is 1.5 km/h. What is the swimmer's upstream speed?

Introduction / Context:
Given a downstream speed and the current, we can recover the still water speed and then compute the upstream speed. This is a standard inverse application of relative speed in a stream.

Given Data / Assumptions:

• Downstream speed u + v = 11 km/h
• Stream speed v = 1.5 km/h
• Uniform straight current

Concept / Approach:
Compute u = (downstream + upstream)/2 is a known identity, but more directly with known downstream and v: u = (u + v) - v. Then upstream speed = u - v.

Step-by-Step Solution:

Verification / Alternative check:
If upstream is 8 and downstream is 11, the still water speed is (8 + 11)/2 = 9.5 km/h, which matches u above.

Why Other Options Are Wrong:

• 9.5 km/h is still water speed, not upstream.
• 9 km/h and 7.5 km/h do not satisfy the given downstream with v = 1.5.
• 6.25 km/h is unrelated to these linear sums.

Common Pitfalls:
Confusing downstream value with still water speed or subtracting twice. Always compute u first, then upstream u - v.

Final Answer:
8 km/h