Boat in still water and current speeds: A man rows at 4 km/h in still water and the rate of the stream is 2 km/h. What is the man's upstream speed against the current (i.e., the effective speed while going against the flow)?

Introduction / Context:
Problems on boats and streams use relative speed. The effective speed upstream equals the still water speed minus the stream speed, while downstream equals the still water speed plus the stream speed. Here we are asked for the upstream speed when still water speed and stream rate are given.

Given Data / Assumptions:

• Speed in still water u = 4 km/h
• Speed of stream v = 2 km/h
• Upstream means boat moves against the current

Concept / Approach:
For boats and streams: upstream speed = u - v and downstream speed = u + v. Units must be consistent in km/h.

Step-by-Step Solution:

Verification / Alternative check:
If we instead computed downstream speed, it would be 4 + 2 = 6 km/h, which is larger than upstream, confirming direction logic is consistent.

Why Other Options Are Wrong:

• 5 km/h and 6 km/h assume addition rather than subtraction or mix the roles of u and v.
• 7 km/h exceeds the still water speed, impossible for upstream.
• 3 km/h does not equal u - v for the given numbers.

Common Pitfalls:
Mixing up upstream and downstream, forgetting units, or subtracting in the wrong order can cause errors. Upstream must be slower than still water speed.

Final Answer:
2 km/h