Still water speed from upstream travel time: A boat covers 12 km upstream in 48 minutes when the stream speed is 2 km/h. What is the speed of the boat in still water?

Introduction / Context:
Upstream speed is reduced by the current. From the upstream distance and time we can find the effective upstream speed and then add back the current to get the still water speed.

Given Data / Assumptions:

• Upstream distance = 12 km
• Upstream time = 48 minutes = 0.8 h
• Stream speed v = 2 km/h

Concept / Approach:
Upstream speed su = distance / time. Then still water u = su + v because su = u - v. Maintain units in km/h.

Step-by-Step Solution:

Verification / Alternative check:
If u = 17 and v = 2, then downstream speed would be 19 km/h. These are reasonable magnitudes around the observed upstream 15 km/h.

Why Other Options Are Wrong:

• 15 km/h is the upstream effective speed, not still water.
• 13 km/h and 12 km/h are too small; adding v must increase from su.
• 19 km/h is the downstream speed u + v, not u.

Common Pitfalls:
Forgetting to convert minutes to hours or subtracting the stream instead of adding to find still water speed. Always express time in hours when speeds are in km/h.

Final Answer:
17 km/h