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Difficulty: MediumLatitude, Longitude, and Time Calculations

A ship captain at sea observes local solar noon (12:00 PM12:00\text{ PM}) on Monday. At that precise moment, a radio time signal from Greenwich (0∘0^\circ) indicates that Greenwich Mean Time (GMT) is 05:20 PM05:20\text{ PM} on Monday. What is the longitude of the ship in degrees West of the Prime Meridian?

Answer: 80 °W

Answer

The longitude of the ship is 80∘W80^\circ\text{W} (80 degrees West).
The time difference between local solar noon (12:00 PM12:00\text{ PM}) and GMT (05:20 PM05:20\text{ PM}) is 5 hours and 20 minutes, or 5135\frac{1}{3} hours. Multiplying 5.333 hours5.333\text{ hours} by 15∘15^\circ per hour yields 80∘80^\circ. Since local solar time is behind GMT, the ship is situated 80∘80^\circ West of the Prime Meridian.

Step-by-Step Solution

1
Calculate the time difference between local solar time and Greenwich Mean Time (GMT)
05:20 PM−12:00 PM=5 hours and 20 minutes=5.333 hours05:20\text{ PM} - 12:00\text{ PM} = 5\text{ hours and } 20\text{ minutes} = 5.333\text{ hours}
The distance in longitude is directly proportional to the difference between local time and GMT.
2
Convert the time difference into angular distance in degrees of longitude
513 hours×15∘/hour=80∘5\frac{1}{3}\text{ hours} \times 15^\circ/\text{hour} = 80^\circ
Earth rotates 360∘360^\circ in 24 hours, which corresponds to 15∘15^\circ of longitude for every 1 hour of time difference.
3
Determine hemisphere direction based on whether local time is ahead or behind GMT
Western Hemisphere (80∘W80^\circ\text{W})
Local time (12:00 PM12:00\text{ PM}) is earlier than GMT (05:20 PM05:20\text{ PM}), placing the ship west of the Prime Meridian.

Key Concept

Calculating longitude using local time and Greenwich Mean Time (GMT)
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Topics

Latitude, Longitude, and Time Calculations

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