A boat travels 64 km downstream in 16 hours and 12 km upstream in 8 hours. What is the speed (in km/hr) of boat in still water?

Options

A. `1.75 `
B. `2.25`
C. `2.75 `
D. `3.25`

Answer

To find the speed of the boat in still water, we can set up the problem using the information given about the boat's travel downstream and upstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let \( x \) be the speed of the boat in still water (in km/hr).
- Let \( y \) be the speed of the stream (in km/hr).

2. **Set Up Equations:**
- When the boat is traveling downstream, its effective speed is \( x + y \).
- When the boat is traveling upstream, its effective speed is \( x - y \).

3. **Use Downstream Information:**
- The boat travels 64 km downstream in 16 hours.
- Using the formula \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \):
\[ x + y = \frac{64 \text{ km}}{16 \text{ hours}} = 4 \text{ km/hr} \quad \text{(Equation 1)} \]

4. **Use Upstream Information:**
- The boat travels 12 km upstream in 8 hours.
- Again using the formula for speed:
\[ x - y = \frac{12 \text{ km}}{8 \text{ hours}} = 1.5 \text{ km/hr} \quad \text{(Equation 2)} \]

5. **Solve the System of Equations:**
- We have the two equations:
1. \( x + y = 4 \)
2. \( x - y = 1.5 \)

- Add both equations to eliminate \( y \):
\[ (x + y) + (x - y) = 4 + 1.5 \]
\[ 2x = 5.5 \quad \Rightarrow \quad x = \frac{5.5}{2} = 2.75 \text{ km/hr} \]

6. **Find the Speed of the Stream:**
- Substitute \( x = 2.75 \) back into Equation 1:
\[ 2.75 + y = 4 \quad \Rightarrow \quad y = 4 - 2.75 = 1.25 \text{ km/hr} \]

7. **Conclusion:**
- The speed of the boat in still water is \( 2.75 \text{ km/hr} \).

### Final Answer:
The speed of the boat in still water is **2.75 km/hr**.