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Difficulty: MediumLatitude, Longitude, and Time Calculations

Two meteorological stations are situated along different meridians. Station Alpha is positioned at longitude 38∘W38^\circ\text{W}, while Station Beta is positioned at longitude 82∘E82^\circ\text{E}. What is the difference in local solar time between these two stations, in hours?

Answer: 8 hours

Answer

The difference in local solar time between the two stations is 8 hours.
Station Alpha is located in the Western Hemisphere (38∘W38^\circ\text{W}) and Station Beta is located in the Eastern Hemisphere (82∘E82^\circ\text{E}). The total angular distance separating them across the Greenwich Meridian is 38∘+82∘=120∘38^\circ + 82^\circ = 120^\circ. Dividing 120∘120^\circ by the Earth's rotation speed of 15∘15^\circ per hour gives a time difference of 8 hours.

Step-by-Step Solution

1
Calculate the total longitudinal angular distance between 38∘W38^\circ\text{W} and 82∘E82^\circ\text{E}.
Angular distance = 38∘+82∘=120∘38^\circ + 82^\circ = 120^\circ.
Because the two locations lie in opposite hemispheres relative to the Prime Meridian (0∘0^\circ), their longitudinal degree values must be added together.
2
Convert the total angular distance to time difference in hours.
Time difference = 120∘÷15∘/hour=8 hours120^\circ \div 15^\circ\text{/hour} = 8\text{ hours}.
The Earth completes a 360∘360^\circ rotation in 24 hours, which corresponds to 15∘15^\circ per hour.

Key Concept

Calculation of longitudinal difference across the Prime Meridian and conversion to local solar time difference.
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Topics

Latitude, Longitude, and Time Calculations

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