To determine when both satellites will be directly over Hawthorne City again after starting at 11:00 AM, we need to follow these steps:
1. Identify the orbit times for each satellite:
- The first satellite completes an orbit every 60 minutes.
- The second satellite completes an orbit every 90 minutes.
2. Find the Least Common Multiple (LCM) of the orbit times:
- The LCM of 60 and 90 is the smallest amount of time after which both satellites will be over the same position simultaneously.
- The LCM of 60 and 90 is 180 minutes, or 3 hours.
3. Calculate the time after 11:00 AM:
- Since the satellites will be over Hawthorne City again 180 minutes (or 3 hours) after 11:00 AM, we add 3 hours to 11:00 AM.
4. Add 3 hours to 11:00 AM:
- 11:00 AM + 3 hours = 2:00 PM.
Therefore, both satellites will pass over Hawthorne City together again at 2:00 PM.
