If the speed of a boat downstream is x km/h and the speed upstream is y km/h them its speed in still water is _______ km/h

Answer

To find the speed of a boat in still water when the speed downstream is \( x \) km/h and the speed upstream is \( y \) km/h, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The speed of the boat downstream is the speed of the boat plus the speed of the current (water flow). This is given as \( x \) km/h.
- The speed of the boat upstream is the speed of the boat minus the speed of the current. This is given as \( y \) km/h.

2. **Set Up the Equations**:
- Let the speed of the boat in still water be \( b \) km/h.
- Let the speed of the current (water flow) be \( w \) km/h.
- From the definitions, we can write two equations:
- Downstream: \( b + w = x \) (1)
- Upstream: \( b - w = y \) (2)

3. **Add the Two Equations**:
- Adding equations (1) and (2):
\[ (b + w) + (b - w) = x + y \]
- This simplifies to:
\[ 2b = x + y \]

4. **Solve for the Speed in Still Water**:
- Divide both sides by 2 to find \( b \):
\[ b = \frac{x + y}{2} \]

5. **Conclusion**:
- The speed of the boat in still water is \( \frac{x + y}{2} \) km/h.

### Final Answer:
The speed of the boat in still water is \( \frac{x + y}{2} \) km/h.

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