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Question

Difficulty: MediumLatitude, Longitude, and Time Calculations

A live radio news program is broadcast from a station in City A, located at longitude 25∘E25^\circ\text{E}, at 03:30 PM03:30\text{ PM} local solar time on Tuesday. What is the local solar time at City B, located at longitude 50∘W50^\circ\text{W}?

  1. 10:30 AM on TuesdayAnswer
  2. B
    08:30 PM on Tuesday
  3. C
    01:50 PM on Tuesday
  4. D
    05:10 PM on Tuesday

Answer

10:30 AM on Tuesday
The total longitudinal separation between 25∘E25^\circ\text{E} and 50∘W50^\circ\text{W} is 75∘75^\circ (25∘+50∘25^\circ + 50^\circ). Since 15∘15^\circ corresponds to 1 hour of solar time, the time difference is 75÷15=5 hours75 \div 15 = 5\text{ hours}. Moving westward from 25∘E25^\circ\text{E} to 50∘W50^\circ\text{W} means local time is earlier, so subtracting 5 hours from 03:30 PM yields 10:30 AM on the same day.

Step-by-Step Solution

1
Calculate the total angular longitudinal difference between City A (25∘E25^\circ\text{E}) and City B (50∘W50^\circ\text{W}).
Since the locations are in opposite hemispheres (East and West), add their longitudes: 25∘+50∘=75∘25^\circ + 50^\circ = 75^\circ.
Distance across the Prime Meridian requires summing the angular distances from 0∘0^\circ longitude.
2
Convert the longitudinal difference into time difference using the Earth's rotation rate (15∘=1 hour15^\circ = 1\text{ hour}).
75∘÷15∘=5 hours75^\circ \div 15^\circ = 5\text{ hours}.
The Earth rotates 360∘360^\circ in 24 hours, which equals 15∘15^\circ per hour.
3
Determine the time direction adjustment and calculate the local solar time at City B.
City B (50∘W50^\circ\text{W}) is west of City A (25∘E25^\circ\text{E}), so subtract 5 hours from 03:30 PM03:30\text{ PM}: 15:30−5:00=10:30 AM15:30 - 5:00 = 10:30\text{ AM} on Tuesday.
Locations to the west are behind in solar time relative to locations to the east ('West subtract, East add').

Key Concept

Longitude and Solar Time Calculation across Hemispheres
Estimated Time:1m 30s
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Topics

Latitude, Longitude, and Time Calculations

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