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 given about the speeds of the boat when rowing downstream and upstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the boat in still water be \( V_1 \) (in km/h).
- Let the speed of the stream be \( V_2 \) (in km/h).

2. **Set Up Equations:**
- When the boat is rowing downstream, the effective speed is the sum of the boat's speed and the stream's speed:
\[ V_1 + V_2 = 15 \quad \text{(1)} \]
- When the boat is rowing upstream, the effective speed is the difference between the boat's speed and the stream's speed:
\[ V_1 - V_2 = 8 \quad \text{(2)} \]

3. **Add the Two Equations:**
- Adding equations (1) and (2):
\[ (V_1 + V_2) + (V_1 - V_2) = 15 + 8 \]
This simplifies to:
\[ 2V_1 = 23 \]

4. **Solve for \( V_1 \):**
- Dividing both sides by 2:
\[ V_1 = \frac{23}{2} = 11.5 \text{ km/h} \]

5. **Substitute \( V_1 \) Back to Find \( V_2 \):**
- Substitute \( V_1 \) back into equation (1):
\[ 11.5 + V_2 = 15 \]
- Rearranging gives:
\[ V_2 = 15 - 11.5 = 3.5 \text{ km/h} \]

6. **Conclusion:**
- The speed of the stream \( V_2 \) is \( 3.5 \text{ km/h} \).

### Final Answer:
The speed of the stream is **3.5 km/h**.