Speed of a boat is 3 km/hr in still water and the speed of the stream is 1 km/hr. If the boat takes 9 hours to go to a place and come back, then what is the distance (in km) of the place?

Options

A. 12
B. 16
C. 18
D. 9

Answer

To solve the problem, we will follow these steps:

### Step 1: Determine the speeds of the boat in downstream and upstream.
- **Downstream speed**: When the boat is going downstream, its speed is the sum of its speed in still water and the speed of the stream.
\[ \text{Downstream speed} = \text{Speed of boat} + \text{Speed of stream} = 3 \text{ km/hr} + 1 \text{ km/hr} = 4 \text{ km/hr} \]

- **Upstream speed**: When the boat is going upstream, its speed is the difference between its speed in still water and the speed of the stream.
\[ \text{Upstream speed} = \text{Speed of boat} - \text{Speed of stream} = 3 \text{ km/hr} - 1 \text{ km/hr} = 2 \text{ km/hr} \]

### Step 2: Set up the time equation.
Let \( D \) be the distance to the place. The time taken to go downstream and the time taken to return upstream can be expressed as:
- Time taken to go downstream:
\[ \text{Time}_{\text{downstream}} = \frac{D}{\text{Downstream speed}} = \frac{D}{4} \]

- Time taken to return upstream:
\[ \text{Time}_{\text{upstream}} = \frac{D}{\text{Upstream speed}} = \frac{D}{2} \]

### Step 3: Total time taken for the round trip.
According to the problem, the total time taken for the round trip is 9 hours:
\[ \text{Time}_{\text{downstream}} + \text{Time}_{\text{upstream}} = 9 \]
Substituting the expressions for time:
\[ \frac{D}{4} + \frac{D}{2} = 9 \]

### Step 4: Solve for \( D \).
To solve the equation, we need a common denominator. The common denominator for 4 and 2 is 4:
\[ \frac{D}{4} + \frac{2D}{4} = 9 \]
Combining the fractions:
\[ \frac{D + 2D}{4} = 9 \]
\[ \frac{3D}{4} = 9 \]
Now, multiply both sides by 4 to eliminate the fraction:
\[ 3D = 36 \]
Now, divide by 3:
\[ D = 12 \]

### Conclusion:
The distance to the place is \( 12 \) km.