Final answer:
At noon at 30° East, the solar time at 20° West would be approximately 8:40 AM, considering the Earth's rotation and the difference of 50° in longitude between the two locations.
Step-by-step explanation:
If it is noon at 30° East, to find the solar time at 20° West, we need to calculate the time difference based on the movement of the Earth relative to the Sun. Given that the Earth rotates at a rate of 15° per hour, every 15° eastward is equivalent to one hour ahead of Greenwich Mean Time (GMT), and conversely, every 15° westward is one hour behind.
Now, the difference in longitude between 30° East and 20° West is 50°, which can be converted into time by dividing by 15° per hour. This gives us a difference of approximately 3 hours and 20 minutes. Since 20° West is to the west of 30° East, the time at 20° West would be earlier. Therefore, if it is noon (12:00 PM) at 30° East, we subtract 3 hours and 20 minutes to find the solar time at 20° West, which would be approximately 8:40 AM.