A boat travels upstream at the speed of 20 km/h and downstream at the speed of 30 km/h. What is the speed of the boat.

Options

A. 26 km/h
B. 25 km/h
C. 24 km/h
D. 22.50 km/h

Answer

To find the speed of the boat, we can use the information provided about its upstream and downstream speeds. Let's break down the solution step by step.

### 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 problem, we know:
- Upstream speed (boat against the current) = \( x - y = 20 \) km/h
- Downstream speed (boat with the current) = \( x + y = 30 \) km/h

### Step 3: Solve the Equations
We have two equations:
1. \( x - y = 20 \) (Equation 1)
2. \( x + y = 30 \) (Equation 2)

Now, we can add these two equations to eliminate \( y \):
\[ (x - y) + (x + y) = 20 + 30 \]
This simplifies to:
\[ 2x = 50 \]

### Step 4: Calculate the Speed of the Boat
Now, divide both sides by 2 to find \( x \):
\[ x = \frac{50}{2} = 25 \text{ km/h} \]

### Conclusion
The speed of the boat in still water is \( 25 \) km/h.