Final answer:
The difference in longitude between the ship's position and its home port is 30 degrees west, because there's a 2-hour difference in local time and each hour corresponds to 15 degrees of longitude.
Step-by-step explanation:
If a clock on a ship indicates that it is 2:00 P.M. in its home port, while another clock on the ship indicates that it is 12:00 noon at the ship's current location, we are looking to find the difference in longitude between the ship's position and its home port. Each hour difference corresponds to 15° of longitude. Since the local time is 12:00 noon and the home port's time is 2:00 P.M., there is a 2-hour difference. Therefore, the ship must be 30° west of the home port, as it is behind in time. This is because time moves ahead as one travels east, and for every 15° of longitude one travels eastward, the local time moves ahead by one hour. Conversely, when traveling westward, the local time moves back, as in this case, which implies the ship is 30° west of its home port.