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Difficulty: MediumLatitude, Longitude, and Time Calculations

Two meteorological observatories, Station Alpha located at longitude 25∘E25^\circ\text{E} and Station Beta located in the Western Hemisphere, measure solar illumination simultaneously. When the local solar time at Station Alpha is 4:30 PM, the local solar time at Station Beta is 11:30 AM on the same day. What is the numerical value of the longitude of Station Beta in degrees West?

Answer: 50 °W

Answer

The longitude of Station Beta is 50∘W50^\circ\text{W}.
Station Alpha is at longitude 25∘E25^\circ\text{E} with local solar time 4:30 PM (16:30). Station Beta records a local solar time of 11:30 AM (11:30) on the same day. The time difference is 16:30−11:30=5 hours16:30 - 11:30 = 5\text{ hours}. Since Earth rotates 15∘15^\circ per hour, a 5-hour time difference corresponds to an angular distance of 5×15∘=75∘5 \times 15^\circ = 75^\circ. Because Station Beta's local time is earlier than Station Alpha's local time, Station Beta is located to the west of Station Alpha. Subtracting 25∘25^\circ to reach the Prime Meridian (0∘0^\circ) leaves 50∘50^\circ west, placing Station Beta at 50∘W50^\circ\text{W}.

Step-by-Step Solution

1
Determine the time difference between the two stations.
Time difference = 16:30 (4:30 PM) - 11:30 (11:30 AM) = 5 hours.
Calculating time separation is the first step in finding angular longitudinal separation.
2
Convert the time difference to angular longitudinal distance using Earth's rotation rate (15∘15^\circ per hour).
Angular distance = 5 hours×15∘/hour=75∘5\text{ hours} \times 15^\circ/\text{hour} = 75^\circ.
The Earth rotates 360∘360^\circ in 24 hours, which equals 15∘15^\circ per hour.
3
Determine the relative direction of Station Beta from Station Alpha.
Station Beta is west of Station Alpha.
Places located further west have earlier local times than places further east.
4
Compute the longitude of Station Beta relative to the Prime Meridian (0∘0^\circ).
Longitude = 75∘−25∘E=50∘W75^\circ - 25^\circ\text{E} = 50^\circ\text{W}.
Moving 25∘25^\circ west from 25∘E25^\circ\text{E} reaches 0∘0^\circ, and the remaining 50∘50^\circ extends west into the Western Hemisphere.

Key Concept

Calculating longitudinal position from local solar time difference across the Prime Meridian
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Topics

Latitude, Longitude, and Time Calculations

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