To find the average distance traveled by the astronauts each hour during their trip to the Moon, we can use the formula:
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} \]
Given:
- Total distance = 238,855 miles
- Total time = 75 hours
Now we can calculate the average speed:
\[ \text{Average speed} = \frac{238,855 \text{ miles}}{75 \text{ hours}} \approx 3,181.0667 \text{ miles per hour} \]
Rounding this to two decimal places gives us approximately 3,181.07 miles per hour. Since none of the provided options exactly match this calculated average speed, the closest correct answer based on rounding and representation is:
3,184.7 \(\overline{3}\) miles (if interpreting the bar properly).
Therefore, based on the provided choices, the average speed at which the astronauts traveled is likely intended to be this option.