Downstream speed of boat is 50 km/h and upstream speed of boat is 30 km/h. Find the speed of boat in still water and speed of stream?

Answer

To solve the problem, we need to find the speed of the boat in still water and the speed of the stream using the given downstream and upstream speeds.

### Step-by-Step Solution:

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

2. **Set Up Equations:**
- The downstream speed of the boat is given as 50 km/h. This can be expressed as:
\[ x + y = 50 \quad \text{(Equation 1)} \]
- The upstream speed of the boat is given as 30 km/h. This can be expressed as:
\[ x - y = 30 \quad \text{(Equation 2)} \]

3. **Add the Two Equations:**
- To eliminate \( y \), we can add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 50 + 30 \]
- This simplifies to:
\[ 2x = 80 \]

4. **Solve for \( x \):**
- Divide both sides by 2:
\[ x = \frac{80}{2} = 40 \text{ km/h} \]
- Thus, the speed of the boat in still water is \( 40 \) km/h.

5. **Substitute \( x \) to Find \( y \):**
- Now, substitute \( x = 40 \) into Equation 1 to find \( y \):
\[ 40 + y = 50 \]
- Rearranging gives:
\[ y = 50 - 40 = 10 \text{ km/h} \]
- Thus, the speed of the stream is \( 10 \) km/h.

### Final Answers:
- Speed of the boat in still water: \( 40 \) km/h
- Speed of the stream: \( 10 \) km/h