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Difficulty: MediumLatitude, Longitude, and Time Calculations

A radio broadcast originates live from City A, located at longitude 10∘W10^\circ\text{W}, at 09:00 AM local time. What is the local time (expressed as an integer in 24-hour clock format, e.g., 14 for 14:00) at City B, located at longitude 65∘E65^\circ\text{E}, when the transmission begins?

Answer: 14 hours

Answer

14
City A (10∘W10^\circ\text{W}) and City B (65∘E65^\circ\text{E}) have a total angular separation of 75∘75^\circ. At the rate of 15∘15^\circ per hour, this equals a 5-hour time difference. Because City B is located to the east of City A, its local time is ahead, so 5 hours added to 09:00 AM gives 14:00 (14).

Step-by-Step Solution

1
Calculate the angular separation between the two longitudes
75∘75^\circ
Since the points lie in different hemispheres (West and East), their longitudinal values must be added together (10∘+65∘=75∘10^\circ + 65^\circ = 75^\circ).
2
Convert angular distance to time difference
5 hours
The Earth rotates 360∘360^\circ in 24 hours, which equals 15∘15^\circ per hour (75∘÷15∘=5 hours75^\circ \div 15^\circ = 5\text{ hours}).
3
Adjust time for directional displacement
14
Travelling eastwards means gaining time because eastern locations experience solar movement earlier. Adding 5 hours to 09:00 AM yields 14:00.

Key Concept

Calculating local time difference across prime meridian boundaries
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Topics

Latitude, Longitude, and Time Calculations

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