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Difficulty: HardThe Earth as a Planet and Earth Movements

City P is located at longitude 38∘E38^\circ\text{E} where the local time is 4:20 p.m. At the exact same moment, the local time at City Q is 9:40 a.m. on the same day. What is the longitude of City Q in degrees West of the Greenwich Meridian?

Answer: 62 degrees West

Answer

City Q is located at longitude 62∘W62^\circ\text{W}.
The calculation demonstrates that a time difference of 6 hours and 40 minutes equals 100∘100^\circ of longitude (400 minutes÷4 minutes/degree400 \text{ minutes} \div 4 \text{ minutes/degree}). Because City Q is earlier in time (9:40 a.m.) than City P (4:20 p.m.), City Q is located 100∘100^\circ to the west of 38∘E38^\circ\text{E}. Subtracting 38∘38^\circ to reach 0∘0^\circ leaves 62∘62^\circ in the Western Hemisphere, giving a final position of 62∘W62^\circ\text{W}.

Step-by-Step Solution

1
Find the local time difference between City P and City Q
Local time difference is 6 hours and 40 minutes (400 minutes)
Converting both times to 24-hour format (16:20 and 09:40) allows direct subtraction: 16:20−09:40=6 h 40 min16:20 - 09:40 = 6\text{ h } 40\text{ min}.
2
Convert time difference into angular longitude difference
Longitude difference is 100∘100^\circ
Earth rotates 1∘1^\circ every 4 minutes. Dividing 400 minutes by 4 yields 100∘100^\circ of total longitude separation.
3
Determine the relative direction of City Q from City P
City Q is located 100∘100^\circ west of City P
Places with earlier local times lie to the west because the Earth rotates from west to east.
4
Calculate the final longitude position west of Greenwich (0∘0^\circ)
Longitude of City Q is 62∘W62^\circ\text{W}
Moving 100∘100^\circ west from 38∘E38^\circ\text{E} covers 38∘38^\circ to reach 0∘0^\circ, and the remaining 62∘62^\circ extends into the Western Hemisphere (100∘−38∘=62∘100^\circ - 38^\circ = 62^\circ).

Key Concept

Calculation of longitude position using local time differences across the Prime Meridian
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Topics

The Earth as a Planet and Earth Movements

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