Explanation:

- A man rows 78 km downstream and 42 km upstream in 6 hours.

- The speed of the stream is 6 km/h.

- Let \( x \) be the speed of the man in still water.

- Downstream speed = \( x + 6 \) and upstream speed = \( x - 6 \).

1. Equation for time:

- Downstream: \( \frac{78}{x + 6} \)

- Upstream: \( \frac{42}{x - 6} \)

- Total time: \( \frac{78}{x + 6} + \frac{42}{x - 6} = 6 \)

2. Solve for \( x \):

- By solving the above equation, we find \( x = 21 \) km/h (man’s speed in still water).

3. Time to row 100 km in still water:

- Time = \( \frac{100}{21} \approx 4.76 \) hours, closer to 5 hours.

- Option 1: 5 hours

- Option 2: 4 hours

- Option 3: 6 hours

- Option 4: 8 hours