Understanding Time Zones and Longitude Calculation

This question asks us to determine the local time at a specific longitude ($90^\circ$ East) given the time at the Greenwich Meridian (0$^\circ$ longitude). The difference in time is directly related to the difference in longitude because the Earth rotates.

Earth's Rotation and Time Differences

• The Earth completes a full rotation of $360^\circ$ in 24 hours.
• This means for every 1 hour, the Earth rotates $15^\circ$ ($360^\circ / 24h = 15^\circ/h$).
• Conversely, for every 1 degree of longitude, the time difference is 4 minutes ($60 \text{ minutes} / 15^\circ = 4 \text{ minutes/}^\circ$).
• Locations to the East of a reference point (like Greenwich) are ahead in time.
• Locations to the West of a reference point are behind in time.

Calculating Time at $90^\circ$ East

We are given:

• Time at Greenwich Meridian (0$^\circ$): 12.00 noon
• Longitude: $90^\circ$ East

First, let's calculate the total time difference based on the longitude:

• Time difference per degree = 4 minutes
• Total time difference = Longitude difference $\times$ Time difference per degree
• Total time difference = $90^\circ \times 4 \text{ min/}^\circ$
• Total time difference = $360$ minutes

Now, convert the total time difference from minutes to hours:

• Time difference in hours = Total minutes / 60
• Time difference in hours = $360 \text{ min} / 60 \text{ min/h}$
• Time difference in hours = $6$ hours

Since $90^\circ$ is East of the Greenwich Meridian, the time there will be ahead of Greenwich time.

Therefore, the time at $90^\circ$ East is:

• Time at $90^\circ$ East = Time at Greenwich Meridian + Time difference
• Time at $90^\circ$ East = 12:00 noon + 6 hours
• Time at $90^\circ$ East = 6:00 PM

Conclusion

When it is 12:00 noon at the Greenwich Meridian, the time at $90^\circ$ East longitude is 6:00 PM.