What is the local time of Pittsburgh, located at 64 degrees East, when GMT is 10:00 AM?
Understand the Problem
The question requires calculating the local time of Pittsburgh, located at 64 degrees East longitude, given that Greenwich Mean Time (GMT) is 10:00 AM. We need to convert the longitudinal difference into a time difference and apply it to the GMT to find the local time.
Answer
2:16 PM
Answer for screen readers
The local time in Pittsburgh is approximately 2:16 PM.
Steps to Solve
- Calculate the longitudinal difference
The longitude of Greenwich is 0 degrees. Pittsburgh is at 64 degrees East. Therefore, the longitudinal difference is $64 - 0 = 64$ degrees.
- Convert the longitudinal difference to time difference
Each 15 degrees of longitude corresponds to 1 hour of time difference. So, we divide the longitudinal difference by 15 to find the time difference in hours: $Time \ Difference = \frac{64}{15} \approx 4.27 \ hours$
- Convert decimal hours to minutes
To convert the decimal part of the hours into minutes, multiply the decimal by 60: $0.27 \ hours \times 60 \ minutes/hour \approx 16 \ minutes$
So, the time difference is approximately 4 hours and 16 minutes.
- Determine the local time
Since Pittsburgh is East of Greenwich, its local time is ahead of GMT. Add the time difference to GMT: $10:00 \ AM + 4 \ hours \ 16 \ minutes = 2:16 \ PM$
The local time in Pittsburgh is approximately 2:16 PM.
More Information
The Earth rotates 360 degrees in 24 hours, meaning each degree of longitude corresponds to 4 minutes of time ($24 \ hours \times 60 \ minutes / 360 \ degrees = 4 \ minutes/degree$). Therefore, a location at 64 degrees East is ahead of GMT.
Tips
A common mistake is to subtract the time difference instead of adding it when calculating the time for a location East of Greenwich. Another mistake is incorrectly converting decimal hours to minutes (e.g., assuming 0.5 hours is 5 minutes instead of 30 minutes).
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