A man can row downstream at 14 km/hr and upstream at 9 km/hr. Man's rate in still water is -----

Options

A. 5 km/hr
B. 23 km/hr
C. 11.5 km/hr
D. None of these

Answer

To solve the problem of finding the man's rate in still water, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( x \) be the speed of the man in still water (in km/hr).
- Let \( y \) be the speed of the stream (in km/hr).

2. **Set Up Equations:**
- The speed of the man when rowing downstream (with the current) is given as 14 km/hr. This can be expressed as:
\[ x + y = 14 \quad \text{(Equation 1)} \]
- The speed of the man when rowing upstream (against the current) is given as 9 km/hr. This can be expressed as:
\[ x - y = 9 \quad \text{(Equation 2)} \]

3. **Add the Two Equations:**
- To eliminate \( y \), we can add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 14 + 9 \]
- This simplifies to:
\[ 2x = 23 \]

4. **Solve for \( x \):**
- Divide both sides by 2 to find \( x \):
\[ x = \frac{23}{2} = 11.5 \text{ km/hr} \]

5. **Conclusion:**
- The man's rate in still water is **11.5 km/hr**.