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Question

Difficulty: MediumLatitude, Longitude, and Time Calculations

An international news broadcast takes place at 8:00 PM8:00\text{ PM} local time in Town X, located at longitude 30∘E30^\circ\text{E}. What is the local time in Town Y, located at longitude 45∘W45^\circ\text{W}?

  1. 3:00 PMAnswer
  2. B
    1:00 AM the next day
  3. C
    7:00 PM
  4. D
    9:00 PM

Answer

3:00 PM
Because Town X (30∘E30^\circ\text{E}) and Town Y (45∘W45^\circ\text{W}) are in opposite hemispheres, their angular separation is 30∘+45∘=75∘30^\circ + 45^\circ = 75^\circ. Dividing by 15∘15^\circ per hour yields a time difference of 5 hours5\text{ hours}. Since Town Y is west of Town X, subtracting 5 hours from 8:00 PM8:00\text{ PM} correctly gives 3:00 PM3:00\text{ PM}.

Step-by-Step Solution

1
Calculate the total angular distance between the two longitudes
Since Town X (30∘E30^\circ\text{E}) and Town Y (45∘W45^\circ\text{W}) are in different hemispheres (East and West), add their longitudes: 30∘+45∘=75∘30^\circ + 45^\circ = 75^\circ.
Locations in opposite hemispheres require adding longitudes to determine total angular separation.
2
Convert the angular distance into a time difference
75∘÷15∘/hour=5 hours75^\circ \div 15^\circ/\text{hour} = 5\text{ hours}.
The Earth rotates 360∘360^\circ in 24 hours, which rate equals 15∘15^\circ per hour.
3
Determine the directional adjustment and calculate the target local time
Town Y (45∘W45^\circ\text{W}) is west of Town X (30∘E30^\circ\text{E}), so subtract 5 hours5\text{ hours} from 8:00 PM8:00\text{ PM} (20:0020:00): 20:00−5 hours=15:0020:00 - 5\text{ hours} = 15:00, which is 3:00 PM3:00\text{ PM}.
Time is behind (earlier) as one travels westward.

Key Concept

Calculating Time Differences Across Hemispheres
Estimated Time:1m 30s
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Topics

Latitude, Longitude, and Time Calculations

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