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Difficulty: MediumLatitude, Longitude, and Time Calculations

A weather monitoring station situated at longitude 55∘W55^\circ\text{W} records a local solar time of 08:20 AM08:20\text{ AM}. At the exact same instant, a maritime research vessel logs a local solar time of 02:40 PM02:40\text{ PM}. What is the longitude of the maritime research vessel in degrees East (∘E^\circ\text{E})?

Answer: 40 °E

Answer

The longitude of the maritime research vessel is 40∘E40^\circ\text{E}.
The time difference between 08:20 AM08:20\text{ AM} (55∘W55^\circ\text{W}) and 02:40 PM02:40\text{ PM} (14:4014:40) is 6 hours and 20 minutes6\text{ hours and } 20\text{ minutes}, which equals 380 minutes380\text{ minutes}. At a rate of 4 minutes per degree4\text{ minutes per degree} of longitude, this represents a longitudinal difference of 95∘95^\circ. Since the vessel's local solar time is ahead, it is situated to the East. Measuring 95∘95^\circ East from 55∘W55^\circ\text{W} crosses the Greenwich Meridian (0∘0^\circ) after 55∘55^\circ, placing the vessel at 40∘E40^\circ\text{E}.

Step-by-Step Solution

1
Calculate the time difference between the weather monitoring station and the maritime research vessel.
Time difference = 14:40−08:20=6 hours 20 minutes=380 minutes14:40 - 08:20 = 6\text{ hours } 20\text{ minutes} = 380\text{ minutes}.
Converting 02:40 PM to 24-hour solar time (14:40) allows direct subtraction of the times.
2
Convert the time difference into angular degrees of longitude.
Angular distance = 380 minutes4 minutes per degree=95∘\frac{380\text{ minutes}}{4\text{ minutes per degree}} = 95^\circ.
The Earth rotates 360∘360^\circ in 24 hours, which corresponds to 1∘1^\circ of longitude every 4 minutes.
3
Determine the direction and calculate the vessel's longitude.
95∘ East−55∘ West to Prime Meridian=40∘E95^\circ\text{ East} - 55^\circ\text{ West to Prime Meridian} = 40^\circ\text{E}.
Because the local solar time at the vessel is ahead (later in the day), the vessel is located to the East. Traveling 95∘95^\circ East starting from 55∘W55^\circ\text{W} uses 55∘55^\circ to reach 0∘0^\circ (Prime Meridian), leaving 40∘40^\circ in the Eastern Hemisphere.

Key Concept

Longitude calculation from local solar time difference across the Prime Meridian
Estimated Time:1m 30s
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Topics

Latitude, Longitude, and Time Calculations

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