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Two satellites make one complete orbit around the Earth every 60 and 90 minutes, respectively. If both satellites are directly over Hawthorne City at 11:00 AM, what time will they pass over Hawthorne City again?

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GinnyAnsweridn
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.
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