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Difficulty: Very hardLatitude, Longitude, and Time Calculations

A research station located at longitude 142∘E142^\circ\text{E} records a solar flare observation at 03:16 PM03:16\text{ PM} local solar time. At the exact same instant, an oceanographic vessel records the same solar flare at 07:48 AM07:48\text{ AM} local solar time on the same day. What is the longitude of the oceanographic vessel in degrees East?

Answer: 30 °E

Answer

The longitude of the oceanographic vessel is 30∘E30^\circ\text{E}.
The research station's local solar time is 15:16 and the oceanographic vessel's time is 07:48, giving a difference of 7 hours 28 minutes (448 minutes). Since 1∘1^\circ of longitude corresponds to 4 minutes of time, the longitudinal difference is 448÷4=112∘448 \div 4 = 112^\circ. Because the vessel's local solar time is earlier than that of the research station, the vessel is located to the west of the research station (142∘E−112∘=30∘E142^\circ\text{E} - 112^\circ = 30^\circ\text{E}).

Step-by-Step Solution

1
Convert both local solar times to 24-hour time format and subtract to determine the exact time difference
Research station time = 15:16, Vessel time = 07:48. Time difference = 7 hours 28 minutes (448 minutes).
Converting to 24-hour format simplifies direct subtraction to evaluate the total time delta between the two locations.
2
Convert the total time difference in minutes to angular longitudinal distance
448 minutes ÷ 4 minutes per degree = 112° difference in longitude.
Earth rotates 360° in 24 hours (1440 minutes), establishing a rate of 1° longitude change per 4 minutes of local time difference.
3
Evaluate direction of location and subtract angular distance from the station's longitude
Vessel time is behind station time, placing it west of the station: 142°E - 112° = 30°E.
Places located further west experience earlier local solar time. Subtracting 112° from 142°E yields 30°E.

Key Concept

Longitude and Time Calculations (converting solar time difference to longitudinal angular distance)
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Topics

Latitude, Longitude, and Time Calculations

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