A boat is rowed downstream at 15 km/h and upstream at 8 km/h. The speed of the stream is:

Options

A. 3.5 km/h
B. 5.5 km/h
C. 6.5 km/h
D. 7.5 km/h

Answer

To find the speed of the stream, we can use the information provided about the boat's speed downstream and upstream.

### Step-by-Step Solution:

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

2. **Set Up Equations**:
- When the boat is going downstream, its effective speed is the sum of its speed in still water and the speed of the stream:
\[ x + y = 15 \quad \text{(1)} \]
- When the boat is going upstream, its effective speed is the difference between its speed in still water and the speed of the stream:
\[ x - y = 8 \quad \text{(2)} \]

3. **Solve the Equations**:
- We can add equations (1) and (2) to eliminate \( y \):
\[ (x + y) + (x - y) = 15 + 8 \]
\[ 2x = 23 \]
\[ x = \frac{23}{2} = 11.5 \text{ km/h} \]

4. **Substitute to Find \( y \)**:
- Now substitute \( x \) back into equation (1) to find \( y \):
\[ 11.5 + y = 15 \]
\[ y = 15 - 11.5 = 3.5 \text{ km/h} \]

5. **Conclusion**:
- The speed of the stream is \( 3.5 \) km/h.