A man moves downstream at a rate of 14 km/h and upstream at a rate of 6 km/h. Speed of boat in still water is

Options

A. 4 km/h
B. 10 km/h
C. 16 km/h
D. 2 km/h

Answer

To find the speed of the boat in still water, we can use the given speeds of the boat moving downstream and upstream.

### Step-by-Step Solution:

1. **Define Variables**:
Let:
- \( x \) = speed of the boat in still water (in km/h)
- \( y \) = speed of the stream (in km/h)

2. **Set Up Equations**:
- When moving downstream, the effective speed is the sum of the speed of the boat and the speed of the stream:
\[ x + y = 14 \quad \text{(1)} \]
- When moving upstream, the effective speed is the difference between the speed of the boat and the speed of the stream:
\[ x - y = 6 \quad \text{(2)} \]

3. **Solve the Equations**:
- We can add equations (1) and (2) to eliminate \( y \):
\[ (x + y) + (x - y) = 14 + 6 \]
\[ 2x = 20 \]
\[ x = 10 \quad \text{(speed of the boat in still water)} \]

4. **Find the Speed of the Stream**:
- Substitute \( x = 10 \) back into equation (1) to find \( y \):
\[ 10 + y = 14 \]
\[ y = 4 \quad \text{(speed of the stream)} \]

5. **Conclusion**:
The speed of the boat in still water is \( 10 \) km/h.

### Final Answer:
The speed of the boat in still water is **10 km/h**.

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