The speed of a boat in still water is 6 kmph and the speed of the stream is 1.5 kmph .A man rows to a place at a distance of 22. 5 km and comes back to the starting point . The total time taken him is :

Options

A. 10 hours
B. 4 hours 10 minutes
C. 6 hours 10 minutes
D. 8 hours

Answer

To solve the problem, we need to calculate the total time taken by the man to row to a place 22.5 km away and return to the starting point, taking into account the speed of the boat in still water and the speed of the stream.

### Step-by-Step Solution:

1. **Identify the Speeds**:
- Speed of the boat in still water = 6 km/h
- Speed of the stream = 1.5 km/h

2. **Calculate Effective Speeds**:
- **Downstream Speed** (when rowing with the stream):
\[ \text{Downstream Speed} = \text{Speed of boat} + \text{Speed of stream} = 6 \text{ km/h} + 1.5 \text{ km/h} = 7.5 \text{ km/h} \]
- **Upstream Speed** (when rowing against the stream):
\[ \text{Upstream Speed} = \text{Speed of boat} - \text{Speed of stream} = 6 \text{ km/h} - 1.5 \text{ km/h} = 4.5 \text{ km/h} \]

3. **Calculate Time Taken for Each Leg of the Journey**:
- **Time taken to row downstream** (to the place):
\[ \text{Distance} = 22.5 \text{ km} \]
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{22.5 \text{ km}}{7.5 \text{ km/h}} = 3 \text{ hours} \]
- **Time taken to row upstream** (back to the starting point):
\[ \text{Time} = \frac{22.5 \text{ km}}{4.5 \text{ km/h}} = 5 \text{ hours} \]

4. **Calculate Total Time Taken**:
\[ \text{Total Time} = \text{Time downstream} + \text{Time upstream} = 3 \text{ hours} + 5 \text{ hours} = 8 \text{ hours} \]

### Final Answer:
The total time taken by the man to row to the place and back to the starting point is **8 hours**.