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Difficulty: MediumLatitude, Longitude, and Time Calculations

A solar eclipse reaches maximum totality in Town P, located at longitude 15∘W15^\circ\text{W}, at 11:20 AM11:20\text{ AM} local time. What is the local time in Town Q, located at longitude 45∘E45^\circ\text{E}, at that exact moment?

  1. 3:20 PM3:20\text{ PM}Answer
  2. B
    7:20 AM7:20\text{ AM}
  3. C
    1:20 PM1:20\text{ PM}
  4. D
    9:20 AM9:20\text{ AM}

Answer

The local time in Town Q is 3:20 PM3:20\text{ PM}.
Because Town P (15∘W15^\circ\text{W}) and Town Q (45∘E45^\circ\text{E}) are in opposite hemispheres, the total longitudinal distance between them is 15∘+45∘=60∘15^\circ + 45^\circ = 60^\circ. Since 15∘15^\circ equals 11 hour of time difference, 60∘60^\circ equals 44 hours. Because Town Q is situated east of Town P, time is ahead in Town Q. Adding 44 hours to 11:20 AM11:20\text{ AM} yields 3:20 PM3:20\text{ PM}.

Step-by-Step Solution

1
Calculate the total longitudinal difference between Town P (15∘W15^\circ\text{W}) and Town Q (45∘E45^\circ\text{E}).
Longitudinal difference =15∘+45∘=60∘= 15^\circ + 45^\circ = 60^\circ.
Since the towns are in opposite hemispheres (West and East), their longitudes are added to find the total angular distance.
2
Convert the longitudinal difference into time.
Time difference =60∘÷15∘/hour=4 hours= 60^\circ \div 15^\circ/\text{hour} = 4\text{ hours}.
The Earth rotates 15∘15^\circ per hour (1∘1^\circ every 44 minutes).
3
Determine the time in Town Q relative to Town P.
Local time in Town Q =11:20 AM+4 hours=3:20 PM= 11:20\text{ AM} + 4\text{ hours} = 3:20\text{ PM}.
Town Q lies to the east of Town P, so its time is ahead of Town P's local time.

Key Concept

Longitude and Time Calculations Across Meridians
Estimated Time:1m 30s
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Topics

Latitude, Longitude, and Time Calculations

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