A man can swim at 8 kmph in still water. He covers an equal distance of 18 km both in upstream and downstream between two points in 6 hours. Find the speed of stream .

Options

A. 5 km/h
B. 6 km/h
C. 7 km/h
D. 4 km/h

Explanation

To solve the problem, we need to find the speed of the stream when a man swims in still water at 8 km/h and covers 18 km both upstream and downstream in a total time of 6 hours.

### Step-by-Step Solution:

1. **Define Variables:**
- Let the speed of the stream be \( x \) km/h.
- The speed of the man in still water is given as 8 km/h.

2. **Calculate Upstream and Downstream Speeds:**
- Upstream speed = Speed in still water - Speed of stream = \( 8 - x \) km/h.
- Downstream speed = Speed in still water + Speed of stream = \( 8 + x \) km/h.

3. **Use the Formula for Time:**
- Time = Distance / Speed.
- The distance covered in both upstream and downstream is 18 km.

4. **Set Up the Time Equation:**
- Time taken to swim upstream = \( \frac{18}{8 - x} \).
- Time taken to swim downstream = \( \frac{18}{8 + x} \).
- The total time for both upstream and downstream is given as 6 hours:
\[ \frac{18}{8 - x} + \frac{18}{8 + x} = 6 \]

5. **Simplify the Equation:**
- Multiply through by the common denominator, \( (8 - x)(8 + x) \):
\[ 18(8 + x) + 18(8 - x) = 6(8^2 - x^2) \]
- This simplifies to:
\[ 18(8 + x + 8 - x) = 6(64 - x^2) \]
- Further simplification gives:
\[ 18 \times 16 = 6(64 - x^2) \]
- Thus:
\[ 288 = 384 - 6x^2 \]

6. **Rearranging the Equation:**
- Move all terms to one side:
\[ 6x^2 = 384 - 288 \]
- This simplifies to:
\[ 6x^2 = 96 \]

7. **Solve for \( x^2 \):**
- Divide both sides by 6:
\[ x^2 = 16 \]
- Taking the square root gives:
\[ x = 4 \text{ km/h} \]

8. **Conclusion:**
- The speed of the stream is \( 4 \) km/h.