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Difficulty: EasyLatitude, Longitude, and Time Calculations

Town P is located at longitude 60∘E60^\circ\text{E}, where the local solar time is 12:00 noon12:00\text{ noon}. Town Q is located at longitude 15∘W15^\circ\text{W}. What is the local solar time at Town Q, expressed as the hour of the day in 24-hour time?

Answer: 7 hours

Answer

The local solar time at Town Q is 7:00 (represented by the number 7).
To find the local time at Town Q (15∘W15^\circ\text{W}) relative to Town P (60∘E60^\circ\text{E} at 12:00 noon12:00\text{ noon}), calculate the longitudinal distance: 60∘+15∘=75∘60^\circ + 15^\circ = 75^\circ. Dividing by 15∘15^\circ per hour gives a time difference of 5 hours5\text{ hours}. Because Town Q is west of Town P, subtract 5 hours from 12:00 to obtain 7:00 (77).

Step-by-Step Solution

1
Calculate the longitudinal difference between Town P and Town Q.
Total angular separation = 60∘E+15∘W=75∘60^\circ\text{E} + 15^\circ\text{W} = 75^\circ.
Locations in opposite hemispheres (East and West) require adding their longitude values to determine total angular distance.
2
Convert the angular distance into hours.
Time difference = 75∘÷15∘/hour=5 hours75^\circ \div 15^\circ/\text{hour} = 5\text{ hours}.
Earth rotates 360∘360^\circ in 24 hours, which corresponds to 15∘15^\circ per hour.
3
Adjust time based on relative position.
Local time at Town Q = 12:00−5 hours=7:0012:00 - 5\text{ hours} = 7:00 (77).
Town Q lies to the west of Town P, so its local time is behind that of Town P.

Key Concept

Calculating local solar time across different longitudes in opposite hemispheres.
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Topics

Latitude, Longitude, and Time Calculations

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