Speeds of a boat along the current and against the current are 14 km/hr and 7 km/hr respectively .What is the speed (in km/ hr ) of the current ?

Options

A. 3.5
B. 1.5
C. 2.5
D. 3

Answer

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

### Step-by-step Solution:

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

2. **Set Up Equations**:
- When the boat is moving along the current, the effective speed is the sum of the speed of the boat and the speed of the current:
\[ y + x = 14 \quad \text{(1)} \]
- When the boat is moving against the current, the effective speed is the difference between the speed of the boat and the speed of the current:
\[ y - x = 7 \quad \text{(2)} \]

3. **Solve the Equations**:
- We can add equations (1) and (2) to eliminate \( x \):
\[ (y + x) + (y - x) = 14 + 7 \]
This simplifies to:
\[ 2y = 21 \]
Therefore,
\[ y = \frac{21}{2} = 10.5 \quad \text{(speed of the boat in still water)} \]

4. **Substitute Back to Find \( x \)**:
- Now, substitute \( y = 10.5 \) into equation (1):
\[ 10.5 + x = 14 \]
Solving for \( x \):
\[ x = 14 - 10.5 = 3.5 \quad \text{(speed of the current)} \]

5. **Final Answer**:
- The speed of the current is \( 3.5 \) km/hr.