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Difficulty: MediumLatitude, Longitude, and Time Calculations

An international flight departs from City P, located at longitude 15∘E15^\circ\text{E}, at 09:15 AM09:15\text{ AM} local solar time. At that precise instant, what is the local solar time at City Q, located at longitude 75∘W75^\circ\text{W}?

  1. 03:15 AM03:15\text{ AM}Answer
  2. B
    03:15 PM03:15\text{ PM}
  3. C
    05:15 AM05:15\text{ AM}
  4. D
    01:15 PM01:15\text{ PM}

Answer

The local solar time at City Q is 03:15 AM03:15\text{ AM}.
Because City P (15∘E15^\circ\text{E}) and City Q (75∘W75^\circ\text{W}) are in opposite hemispheres, the angular separation is 15∘+75∘=90∘15^\circ + 75^\circ = 90^\circ. Since 15∘15^\circ equals 1 hour of time difference, 90∘90^\circ equals 6 hours. Moving from East to West requires subtracting the time difference: 09:15 AM−6 hours=03:15 AM09:15\text{ AM} - 6\text{ hours} = 03:15\text{ AM}.

Step-by-Step Solution

1
Calculate total longitudinal distance between City P (15∘E15^\circ\text{E}) and City Q (75∘W75^\circ\text{W}).
Longitudinal difference = 15∘+75∘=90∘15^\circ + 75^\circ = 90^\circ.
When locations are in opposite hemispheres (East and West), their longitudinal values are added to find total angular separation.
2
Convert the longitudinal difference into a time difference.
Time difference = 90∘÷15∘/hour=6 hours90^\circ \div 15^\circ\text{/hour} = 6\text{ hours}.
Earth rotates 360∘360^\circ in 24 hours, which corresponds to 15∘15^\circ of longitude per hour.
3
Adjust time based on direction of movement.
09:15 AM−6 hours=03:15 AM09:15\text{ AM} - 6\text{ hours} = 03:15\text{ AM}.
Places to the west of a reference meridian are behind in time ('West subtract'), so the time difference must be subtracted.

Key Concept

Longitude and Solar Time Calculations
Estimated Time:1m 30s
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Topics

Latitude, Longitude, and Time Calculations

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