A cargo vessel positioned at longitude 45^\circ\text{W} reports a local solar time of 10:3… — JAMB UTME

A cargo vessel positioned at longitude $45^\circ\text{W}$ reports a local solar time of $10:30\text{ AM}$ . At that precise moment, a coastal harbor records a local solar time of $03:30\text{ PM}$ . What is the longitude of the coastal harbor in degrees East ( $^\circ\text{E}$ )?

Answer: 30 degrees East

Answer

The longitude of the coastal harbor is 30 degrees East (30°E).

Because the harbor is experiencing a later local solar time (03:30 PM) than the vessel (10:30 AM), it must lie to the East of the vessel. The 5-hour time difference equates to an angular distance of 75°. Crossing from 45°W past the Greenwich Meridian (0°) leaves 30° in the Eastern Hemisphere, placing the harbor at 30°E.

Step-by-Step Solution

Calculate time difference

5 hours

The difference between 10:30 AM and 03:30 PM (15:30) is 5 hours.

Convert time difference to longitudinal angular distance

75 degrees

Earth rotates 15 degrees per hour, so 5 hours corresponds to 5 × 15° = 75°.

Calculate position relative to Prime Meridian

30 degrees East

Moving East from 45°W by 75° requires traversing 45° to reach 0° (Greenwich Meridian), and the remaining 30° extends into the Eastern Hemisphere.

Key Concept

Longitude and Time Calculations across Hemispheres

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