The speed of boat upstream and speed of boat downstream are 7 km/h and 13 km/h, respectively. Find the speed of stream and speed of boat in still water.

Options

A. 5 km/h, 10 km/h
B. 10 km/h, 5 km/h
C. 3km/h, 10km/h
D. 13 km/h, 3 km/h

Answer

To solve the problem of finding the speed of the boat in still water and the speed of the stream, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = speed of the boat in still water (in km/h)
- \( y \) = speed of the stream (in km/h)

### Step 2: Set Up Equations
From the information given:
1. The speed of the boat upstream is given by the equation:
\[ x - y = 7 \quad \text{(Equation 1)} \]
2. The speed of the boat downstream is given by the equation:
\[ x + y = 13 \quad \text{(Equation 2)} \]

### Step 3: Solve the Equations
We can solve these two equations simultaneously.

**Adding Equation 1 and Equation 2:**
\[ (x - y) + (x + y) = 7 + 13 \]
This simplifies to:
\[ 2x = 20 \]
Now, divide both sides by 2:
\[ x = 10 \quad \text{(Speed of the boat in still water)} \]

### Step 4: Substitute to Find \( y \)
Now that we have \( x \), we can substitute it back into either equation to find \( y \). Let's use Equation 1:
\[ 10 - y = 7 \]
Subtract 10 from both sides:
\[ -y = 7 - 10 \]
\[ -y = -3 \]
Now, multiply both sides by -1:
\[ y = 3 \quad \text{(Speed of the stream)} \]

### Conclusion
The speed of the boat in still water is \( 10 \) km/h and the speed of the stream is \( 3 \) km/h.

### Summary of Results
- Speed of the boat in still water (\( x \)): **10 km/h**
- Speed of the stream (\( y \)): **3 km/h**

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