A boat goes 48 km downstream in 20 h.It takes 4 h more to cover the same distance against the stream. What is the speed of the boat in still water?

Options

A. 2.2 km/h
B. 2 km/h
C. 4 km/h
D. 4.2 km/h

Answer

To solve the problem step by step, we need to find the speed of the boat in still water based on the information given about its journey downstream and upstream.

### 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: Determine Downstream Speed
The speed of the boat downstream (with the current) is:
\[ x + y \]

### Step 3: Determine Upstream Speed
The speed of the boat upstream (against the current) is:
\[ x - y \]

### Step 4: Use the Downstream Information
We know the boat travels 48 km downstream in 20 hours. Using the formula for speed:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
We can write:
\[ x + y = \frac{48 \text{ km}}{20 \text{ h}} = 2.4 \text{ km/h} \]

### Step 5: Use the Upstream Information
It takes 4 hours more to cover the same distance upstream. Therefore, the time taken upstream is:
\[ 20 \text{ hours} + 4 \text{ hours} = 24 \text{ hours} \]
Using the same speed formula for upstream:
\[ x - y = \frac{48 \text{ km}}{24 \text{ h}} = 2 \text{ km/h} \]

### Step 6: Set Up the Equations
Now we have two equations:
1. \( x + y = 2.4 \) (1)
2. \( x - y = 2 \) (2)

### Step 7: Solve the Equations
To solve for \( x \) and \( y \), we can add equations (1) and (2):
\[ (x + y) + (x - y) = 2.4 + 2 \]
This simplifies to:
\[ 2x = 4.4 \]
Thus, dividing both sides by 2 gives:
\[ x = 2.2 \text{ km/h} \]

### Step 8: Find the Speed of the Stream
Now substitute \( x = 2.2 \) back into equation (1):
\[ 2.2 + y = 2.4 \]
This simplifies to:
\[ y = 2.4 - 2.2 = 0.2 \text{ km/h} \]

### Conclusion
The speed of the boat in still water is:
\[ \boxed{2.2 \text{ km/h}} \]