Compute upstream speed given downstream and stream: The downstream speed of a boat is 15 km/h and the stream speed is 1.5 km/h. What is the upstream speed?

Introduction / Context:
Given downstream speed (u + v) and current v, recover still-water speed u, then compute the upstream speed u − v. Linear relations make this a direct two-step substitution.

Given Data / Assumptions:

• Downstream speed u + v = 15 km/h.
• Stream speed v = 1.5 km/h.

Concept / Approach:
First find u = 15 − 1.5 = 13.5. Then upstream speed is u − v.

Step-by-Step Solution:
u = 15 − 1.5 = 13.5 km/h.Upstream = u − v = 13.5 − 1.5 = 12 km/h.

Verification / Alternative check:
Check symmetry: average of up and down is (12 + 15)/2 = 13.5, which equals u.

Why Other Options Are Wrong:
13.5 is u, not upstream; 16.5 exceeds downstream; 8.25 and 11 contradict u = 13.5.

Common Pitfalls:
Answering with u instead of upstream; subtracting v twice or forgetting to subtract at all.

Final Answer:
12 km/hr