Final answer:
To find your longitude based on GMT and local time differences, remember that every 15 degrees of longitude represents a one-hour difference from GMT. By analyzing the time differences provided, one can deduce their longitudinal position on the Earth relative to the prime meridian.
Step-by-step explanation:
Understanding time in relation to longitude and Greenwich Mean Time (GMT) requires grasping that every 15° of longitude represents one hour's difference from GMT. To determine your position in relation to GMT, you need to examine the difference between GMT and your local time. If you're located to the east of Greenwich, your local time is ahead of GMT, and if you're to the west, it's behind GMT.
1. If it's 3 pm GMT and 5 pm local time, you are 2 hours ahead of GMT. This means you are at 30° east longitude (15° for each hour).
2. If it's 10 pm local time and 7 pm GMT, then you are 3 hours ahead of GMT, placing you at 45° east longitude.
3. If it's 1 pm GMT and you're located on the 30° WEST longitude line, it is 10 am for you, because you're 3 hours behind GMT.
4. When a ship at the prime meridian finds Polaris at an altitude of 45 degrees, this indicates that the ship's latitude is also 45 degrees. The longitude is 0°, as it's at the prime meridian.
5. If it's 2 pm GMT and 9 am local time, you're 5 hours behind GMT. You are therefore located at 75° west longitude.