Final answer:
To determine the longitude, we calculate the time difference between local sunrise and sunrise in Greenwich, then convert the hours and minutes into degrees. Since sunrise at the given location is 6 hours and 58 minutes after it is in Greenwich, this corresponds to a longitude of 104.5 degrees east.
Step-by-step explanation:
The question is asking to determine the longitude of a location where local sunrise, when converted to Greenwich Mean Time (GMT), is at 14:31 (2:31 p.m.). To solve this, we know that the Earth is divided into 24 time zones, each 15 degrees of longitude wide. The prime meridian, located at the Royal Observatory in Greenwich, England, represents the point where longitude begins, at 0 degrees.
For every 15 degrees of longitude to the east of Greenwich, local time is one hour ahead of GMT. Conversely, for every 15 degrees of longitude to the west, local time is one hour behind GMT. Since the given local sunrise time is at 14:31 GMT and sunrise in Greenwich is at 7:33 GMT, the time difference is 6 hours and 58 minutes. Since one hour represents 15 degrees, we calculate the degrees for the full hours first (6 × 15 degrees = 90 degrees) and then convert the remaining 58 minutes to a fraction of an hour to find the additional degrees of longitude (58 minutes is approximately 0.967 decimal hours × 15 degrees/hour = 14.5 degrees).
Therefore, the longitude of the given location is 90 degrees + 14.5 degrees, which is 104.5 degrees. Assuming the sunset occurs afterwards and taking into account the direction of Earth's rotation, we can conclude that the location is 104.5 degrees east of Greenwich.