A man can row 4.5 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream.

Options

A. 1.5 km/hr
B. 2 km/hr
C. 2.5 km/hr
D. 1.75 km/hr

Answer

To solve the problem, we need to find the speed of the stream based on the information given about the man's rowing speed in still water and the time taken to row upstream and downstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the stream be \( x \) km/hr.
- The speed of the man in still water is given as \( 4.5 \) km/hr.

2. **Calculate Speeds:**
- **Upstream Speed:** When rowing upstream (against the current), the effective speed will be \( 4.5 - x \) km/hr.
- **Downstream Speed:** When rowing downstream (with the current), the effective speed will be \( 4.5 + x \) km/hr.

3. **Set Up the Time Relationship:**
- Let the distance traveled in both directions be \( y \) km.
- The time taken to row upstream is given by:
\[ \text{Time upstream} = \frac{y}{4.5 - x} \]
- The time taken to row downstream is given by:
\[ \text{Time downstream} = \frac{y}{4.5 + x} \]
- According to the problem, the time taken to row upstream is twice the time taken to row downstream:
\[ \frac{y}{4.5 - x} = 2 \cdot \frac{y}{4.5 + x} \]

4. **Eliminate \( y \):**
- Since \( y \) is common in both terms, we can cancel it out (assuming \( y \neq 0 \)):
\[ \frac{1}{4.5 - x} = \frac{2}{4.5 + x} \]

5. **Cross Multiply:**
- Cross multiplying gives:
\[ 4.5 + x = 2(4.5 - x) \]
- Expanding the right side:
\[ 4.5 + x = 9 - 2x \]

6. **Rearranging the Equation:**
- Bring all terms involving \( x \) to one side:
\[ x + 2x = 9 - 4.5 \]
\[ 3x = 4.5 \]

7. **Solve for \( x \):**
- Divide both sides by 3:
\[ x = \frac{4.5}{3} = 1.5 \text{ km/hr} \]

### Conclusion:
The speed of the stream is \( 1.5 \) km/hr.