A boat travesl 32 km downstream in 4 hours and 24 km upstream in 6 hours .What is the speed (in km/hr) of boat in still water ?

Options

A. 2
B. 4
C. 6
D. 8

Answer

To solve the problem, we need to find the speed of the boat in still water. We will use the information given about the distances traveled downstream and upstream, along with the time taken for each journey.

### Step-by-step Solution:

1. **Determine the speeds downstream and upstream:**
- The boat travels 32 km downstream in 4 hours.
- Speed downstream = Distance / Time = 32 km / 4 hours = 8 km/hr.

- The boat travels 24 km upstream in 6 hours.
- Speed upstream = Distance / Time = 24 km / 6 hours = 4 km/hr.

2. **Let the speed of the boat in still water be \( x \) km/hr and the speed of the stream be \( y \) km/hr.**
- The speed downstream can be expressed as:
\[ x + y = 8 \quad \text{(1)} \]
- The speed upstream can be expressed as:
\[ x - y = 4 \quad \text{(2)} \]

3. **Add equations (1) and (2):**
\[ (x + y) + (x - y) = 8 + 4 \]
\[ 2x = 12 \]
\[ x = 6 \quad \text{(Speed of the boat in still water)} \]

4. **Substitute \( x \) back into one of the equations to find \( y \):**
- Using equation (1):
\[ 6 + y = 8 \]
\[ y = 2 \quad \text{(Speed of the stream)} \]

5. **Conclusion:**
- The speed of the boat in still water is **6 km/hr**.