A man can row upstream at 10 km/hr, and downstream at 16 km/hr. Find the rate of the current?

Answer

To find the rate of the current, we can use the information provided about the man's rowing speeds upstream and downstream. Let's break down the solution step by step.

### 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 current (in km/hr).

2. **Set Up Equations:**
- When rowing downstream, the speed of the man is the sum of his speed in still water and the speed of the current:
\[ x + y = 16 \quad \text{(1)} \]
- When rowing upstream, the speed of the man is the difference between his speed in still water and the speed of the current:
\[ x - y = 10 \quad \text{(2)} \]

3. **Add the Two Equations:**
- Adding equations (1) and (2):
\[ (x + y) + (x - y) = 16 + 10 \]
\[ 2x = 26 \]
- Solving for \( x \):
\[ x = \frac{26}{2} = 13 \quad \text{(Speed of the man in still water)} \]

4. **Substitute \( x \) Back to Find \( y \):**
- Substitute \( x = 13 \) into equation (1):
\[ 13 + y = 16 \]
- Solving for \( y \):
\[ y = 16 - 13 = 3 \quad \text{(Speed of the current)} \]

5. **Conclusion:**
- The rate of the current is \( 3 \) km/hr.

### Final Answer:
The rate of the current is **3 km/hr**.