To determine the time in Mecca, which is located at 40° East longitude, when the time at the Prime Meridian (0° longitude) is 12:00 am (midnight), follow these steps:
1. Understand Earth's Rotation and Time Zones:
- The Earth rotates 360 degrees in 24 hours.
- Hence, it completes 15 degrees of rotation in one hour (360 degrees / 24 hours = 15 degrees per hour).
2. Calculate the Time Difference:
- Mecca is at 40° East longitude.
- To find the time difference, divide the longitude of Mecca by the degrees per hour:
[tex]\[
\text{Time Difference} = \frac{40^\circ}{15^\circ/\text{hour}} = 2.\overline{666} \, (\text{or} \, 2 \, hours \, and \, 40 \, minutes)
\][/tex]
3. Determine the Time in Mecca:
- Since Mecca is located to the east of the Prime Meridian, the local time in Mecca will be ahead of the Prime Meridian time.
- Adding the calculated time difference to 12:00 am (midnight) results in the time in Mecca:
[tex]\[
12:00 \, \text{am} + 2.\overline{666} \, \text{hours} = 2:40 \, \text{am}
\][/tex]
Thus, when it is 12:00 am at the Prime Meridian (UTC), the local time in Mecca (which is 40° E) is approximately 2:40 am.
