A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?A1 kmphB8 kmphC5 kmphD3 kmph

Break Down the Problem

1. Let the speed of the man in still water be $x$ km/h.
2. Let the speed of the stream be $y$ km/h.
3. When rowing with the stream, the effective speed is $x + y$.
4. When rowing against the stream, the effective speed is $x - y$.

Relevant Concepts

• Given equations: $x + y = 6 \quad (1)$ $x - y = 4 \quad (2)$

Analysis and Detail

1. From equation (1), we have: $y = 6 - x \quad (3)$
2. Substitute equation (3) into equation (2): $x - (6 - x) = 4$ $x - 6 + x = 4$ $2x - 6 = 4$ $2x = 10$ $x = 5 \quad (4)$
3. Substitute $x = 5$ back into equation (3) to find $y$: $y = 6 - 5 = 1$

Verify and Summarize

• The man's rate in still water is $x = 5$ km/h.
• The speed of the stream is $y = 1$ km/h.

Final Answer

The man's rate is $\boxed{5}$ km/h (Option C).