A man can rowdownstream a distance of 9 km in 2 hours and takes 6 hours while returning to the starting point. What is the speed (in km/h) of the stream?

Options

A. 2
B. `2.5`
C. `1.5`
D. 3

Answer

To solve the problem, we need to determine the speed of the stream based on the given information about the man's rowing speeds downstream and upstream.

### Step-by-Step Solution:

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

2. **Determine Downstream and Upstream Speeds**:
- Downstream speed = \( x + y \) (the speed of the man plus the speed of the stream)
- Upstream speed = \( x - y \) (the speed of the man minus the speed of the stream)

3. **Use Given Distances and Times**:
- The man rows downstream a distance of 9 km in 2 hours. Therefore, we can express this as:
\[ \text{Downstream Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{9 \text{ km}}{2 \text{ hours}} = 4.5 \text{ km/h} \]
- The man rows upstream the same distance of 9 km in 6 hours. Therefore, we can express this as:
\[ \text{Upstream Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{9 \text{ km}}{6 \text{ hours}} = 1.5 \text{ km/h} \]

4. **Set Up Equations**:
From the definitions of downstream and upstream speeds, we have:
\[ x + y = 4.5 \quad \text{(1)} \]
\[ x - y = 1.5 \quad \text{(2)} \]

5. **Solve the Equations**:
To find \( x \) and \( y \), we can add equations (1) and (2):
\[ (x + y) + (x - y) = 4.5 + 1.5 \]
This simplifies to:
\[ 2x = 6 \implies x = 3 \text{ km/h} \]

Now, substitute \( x = 3 \) back into equation (1):
\[ 3 + y = 4.5 \implies y = 4.5 - 3 = 1.5 \text{ km/h} \]

6. **Conclusion**:
The speed of the stream \( y \) is \( 1.5 \) km/h.

### Final Answer:
The speed of the stream is **1.5 km/h**.