Speed of a boat along the current and against the current are 12 km/hr and 6 km/hr respectively. What is the speed of boat (in km/hr) in still water?

Options

A. 3
B. 6
C. 9
D. 12

Answer

To find the speed of the boat in still water, we can use the information provided about the speeds of the boat along the current and against the current.

### Step-by-Step Solution:

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

2. **Set Up Equations**:
- When the boat is moving along the current (downstream), its speed is the sum of its speed in still water and the speed of the current:
\[ x + y = 12 \quad \text{(1)} \]
- When the boat is moving against the current (upstream), its speed is the difference between its speed in still water and the speed of the current:
\[ x - y = 6 \quad \text{(2)} \]

3. **Add the Two Equations**:
- By adding equations (1) and (2), we eliminate \( y \):
\[ (x + y) + (x - y) = 12 + 6 \]
\[ 2x = 18 \]

4. **Solve for \( x \)**:
- Divide both sides by 2 to find \( x \):
\[ x = \frac{18}{2} = 9 \]

5. **Conclusion**:
- The speed of the boat in still water is \( 9 \) km/hr.