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Difficulty: HardLatitude, Longitude, and Time Calculations

A navigator on Ship P observes local solar noon (12:00 noon) when a Greenwich Mean Time (GMT) chronometer reads 1:40 PM. If Ship Q is located at a position where the local time is exactly 4 hours ahead of Ship P, what is the longitude of Ship Q?

  1. 35∘E35^\circ\text{E}Answer
  2. B
    35∘W35^\circ\text{W}
  3. C
    85∘E85^\circ\text{E}
  4. D
    85∘W85^\circ\text{W}

Answer

35∘E35^\circ\text{E}
Ship P is at 25∘W25^\circ\text{W} because its local time is 1 hour 40 minutes (100 minutes) behind GMT (100 minutes / 4 min per degree = 25∘W25^\circ\text{W}). Since Ship Q is 4 hours ahead in time, it lies 60∘60^\circ to the east (4×15∘4 \times 15^\circ). Measuring 60∘60^\circ east from 25∘W25^\circ\text{W} covers 25∘25^\circ to reach the Greenwich Meridian (0∘0^\circ), leaving 35∘35^\circ into the Eastern Hemisphere, resulting in 35∘E35^\circ\text{E}.

Step-by-Step Solution

1
Calculate the longitude of Ship P using local time and GMT
Time difference = 1 hour 40 minutes = 100 minutes. Longitude of Ship P = 100 minutes/4 minutes per degree=25∘W100 \text{ minutes} / 4 \text{ minutes per degree} = 25^\circ\text{W} (since local time is behind GMT).
The Earth rotates 1∘1^\circ every 4 minutes, and areas behind GMT are located in the Western Hemisphere.
2
Determine the time difference and direction from Ship P to Ship Q
Time difference = 4 hours ahead. Direction = East of Ship P.
Local time increases as one moves east.
3
Convert the 4-hour time difference into angular distance in degrees
Angular distance = 4 hours×15∘/hour=60∘4 \text{ hours} \times 15^\circ/\text{hour} = 60^\circ.
Earth rotates at a rate of 15∘15^\circ per hour.
4
Calculate the longitude of Ship Q by moving 60∘60^\circ east from 25∘W25^\circ\text{W}
Distance to Greenwich Meridian (0∘0^\circ) = 25∘25^\circ east. Remaining distance east into Eastern Hemisphere = 60∘−25∘=35∘E60^\circ - 25^\circ = 35^\circ\text{E}.
Crossing the Prime Meridian changes the hemisphere designation from West to East.

Key Concept

Longitude calculation using Greenwich Mean Time (GMT) and local time adjustments across meridians
Estimated Time:2m 0s
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Topics

Latitude, Longitude, and Time Calculations

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