A boat’s upstream and downstream speeds are 7 km/h and 13 km/h, respectively. Find the speed of the stream and the speed of the boat in still water.

Introduction / Context:
In boats-and-streams, downstream speed = boat + stream; upstream = boat − stream. Solving the two linear equations yields both unknowns.

Given Data / Assumptions:

• Upstream u = 7 km/h.
• Downstream d = 13 km/h.
• Let boat speed in still water be b and stream speed be s.

Concept / Approach:
Use the identities d = b + s and u = b − s. Adding gives 2b; subtracting gives 2s.

Step-by-Step Solution:

Verification / Alternative check:
Check: b + s = 10 + 3 = 13; b − s = 10 − 3 = 7 (consistent).

Why Other Options Are Wrong:
They either swap values or produce sums/differences that do not match 13 and 7.

Common Pitfalls:
Answering in the wrong order (boat first vs stream first). The asked order is stream, then boat.

Final Answer:
3 km/h and 10 km/h