The speed of a boat in still water is 9 km/hr. It can go 12 km upstream and 12 km downstream in 3 hours. Find the speed of the stream.

Answer

To solve the problem, we need to find the speed of the stream given the speed of the boat in still water and the time taken to travel a certain distance upstream and downstream.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the boat in still water be \( b = 9 \) km/hr.
- Let the speed of the stream be \( x \) km/hr.

2. **Calculate Speeds:**
- The speed of the boat upstream (against the current) is \( b - x = 9 - x \) km/hr.
- The speed of the boat downstream (with the current) is \( b + x = 9 + x \) km/hr.

3. **Calculate Time Taken:**
- The distance traveled upstream is 12 km. The time taken to travel upstream is given by:
\[ \text{Time}_{\text{upstream}} = \frac{12}{9 - x} \]
- The distance traveled downstream is also 12 km. The time taken to travel downstream is given by:
\[ \text{Time}_{\text{downstream}} = \frac{12}{9 + x} \]

4. **Set Up the Equation:**
- According to the problem, the total time taken for both upstream and downstream travel is 3 hours:
\[ \frac{12}{9 - x} + \frac{12}{9 + x} = 3 \]

5. **Simplify the Equation:**
- Divide the entire equation by 12:
\[ \frac{1}{9 - x} + \frac{1}{9 + x} = \frac{1}{4} \]

6. **Find a Common Denominator:**
- The common denominator for the left side is \((9 - x)(9 + x)\):
\[ \frac{(9 + x) + (9 - x)}{(9 - x)(9 + x)} = \frac{1}{4} \]
- Simplifying the numerator gives:
\[ \frac{18}{(9 - x)(9 + x)} = \frac{1}{4} \]

7. **Cross Multiply:**
- Cross multiplying gives:
\[ 18 \cdot 4 = (9 - x)(9 + x) \]
\[ 72 = 81 - x^2 \]

8. **Rearrange the Equation:**
- Rearranging gives:
\[ x^2 = 81 - 72 \]
\[ x^2 = 9 \]

9. **Solve for \( x \):**
- Taking the square root gives:
\[ x = 3 \quad (\text{since speed cannot be negative}) \]

10. **Conclusion:**
- The speed of the stream is \( x = 3 \) km/hr.

### Final Answer:
The speed of the stream is **3 km/hr**.