Final answer:
The date and time at 15° east when it is 10:00 PM on July 3rd at 30° west is July 4th, 1:00 AM, taking into account the 45° longitude difference that equals a three-hour time difference.
Step-by-step explanation:
If it is 10:00 PM on July 3rd at 30° west, to find out the date and time at 15° east, we need to calculate the time difference based on the longitudes provided.
Each 15° of longitude represents one hour of time difference. Since we are moving from 30° west to 15° east, we are crossing 45° of longitude, which equates to a three-hour time difference. Moreover, since east is ahead in time compared to the west, we need to add those three hours to the current time at 30° west.
Starting from 10:00 PM on July 3rd and adding three hours, we get to 1:00 AM on July 4th. So, the correct date and time at 15° east when it is 10:00 PM at 30° west on July 3rd would be July 4th, 1:00 AM.