Rahul can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If the speed of Rahul in still water is 12 km/hr, find the speed of the stream.

Options

A. 2 km/hr
B. 2.4 km/hr
C. 3 km/hr
D. Data inadequate

Answer

To solve the problem step by step, we will use the information given about Rahul's rowing downstream and upstream, and apply the formula for distance, which is:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

### Step 1: Define Variables
Let:
- \( b \) = speed of Rahul in still water = 12 km/hr
- \( w \) = speed of the stream (what we need to find)

### Step 2: Calculate Downstream Speed
When rowing downstream, the effective speed is the sum of Rahul's speed in still water and the speed of the stream:
\[ \text{Downstream Speed} = b + w = 12 + w \]

### Step 3: Calculate Upstream Speed
When rowing upstream, the effective speed is the difference between Rahul's speed in still water and the speed of the stream:
\[ \text{Upstream Speed} = b - w = 12 - w \]

### Step 4: Set Up Distance Equations
The distance traveled downstream in 6 hours can be expressed as:
\[ \text{Distance} = \text{Downstream Speed} \times \text{Time} = (12 + w) \times 6 \]

The distance traveled upstream in 9 hours can be expressed as:
\[ \text{Distance} = \text{Upstream Speed} \times \text{Time} = (12 - w) \times 9 \]

### Step 5: Equate the Distances
Since the distance traveled downstream and upstream is the same, we can set the two equations equal to each other:
\[ (12 + w) \times 6 = (12 - w) \times 9 \]

### Step 6: Expand Both Sides
Expanding both sides gives:
\[ 72 + 6w = 108 - 9w \]

### Step 7: Combine Like Terms
Now, let's move all terms involving \( w \) to one side and constant terms to the other side:
\[ 6w + 9w = 108 - 72 \]
\[ 15w = 36 \]

### Step 8: Solve for \( w \)
Now, divide both sides by 15 to find the speed of the stream:
\[ w = \frac{36}{15} = 2.4 \text{ km/hr} \]

### Final Answer
The speed of the stream is **2.4 km/hr**.

---