Final answer:
The local time at longitude 64 degrees east when the GMT is 10:00 am is 02:00 pm. This is because every 15 degrees of longitude represents a one-hour difference from GMT, and 64 degrees east is approximately 4 hours ahead of GMT.
Step-by-step explanation:
The local time of a place depends on its longitude and the Greenwich Mean Time (GMT) or Universal Time (UT). One hour of time difference corresponds to 15 degrees of longitude. Since there are 24 hours in a day, the Earth is divided into 24 standard time zones, each 15 degrees wide. Every 15 degrees to the east of the Prime Meridian represents one hour ahead of GMT, and every 15 degrees to the west represents one hour behind GMT.
If the GMT is 10:00 am, we calculate the local time at 64 degrees east by dividing the longitude by 15 degrees per hour (64° ÷ 15°/hour = 4.27 hours). Since we can't have a fraction of an hour in time zones, we round it to 4 hours ahead, which means the local time is 4 hours later than GMT. Therefore, if it's 10:00 am GMT, the local time at 64 degrees east would be 02:00 pm.