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Difficulty: MediumLatitude, Longitude, and Time Calculations

Town A is situated at longitude 20∘W20^\circ\text{W}. When the local solar time at Town A is 09:00 AM09:00\text{ AM}, the local solar time at Town B is 01:00 PM01:00\text{ PM} on the same day. What is the longitude of Town B in degrees East?

Answer: 40 °E

Answer

The longitude of Town B is 40°E.
Town B is 4 hours ahead of Town A, which corresponds to an angular distance of 60∘60^\circ East (4×15∘4 \times 15^\circ). Traveling 60∘60^\circ East starting from 20∘W20^\circ\text{W} takes 20∘20^\circ to reach the Prime Meridian (0∘0^\circ), and the remaining 40∘40^\circ places Town B at 40∘E40^\circ\text{E}.

Step-by-Step Solution

1
Calculate the difference in local solar time between Town A and Town B.
Time difference = 13:00−09:00=4 hours13:00 - 09:00 = 4\text{ hours}.
Local solar time differences represent angular distance between meridians.
2
Convert the time difference into degrees of longitude.
4 hours×15∘/hour=60∘4\text{ hours} \times 15^\circ/\text{hour} = 60^\circ longitude difference.
The Earth rotates 360∘360^\circ in 24 hours, which corresponds to 15∘15^\circ of longitude per hour.
3
Determine direction and calculate the exact longitude of Town B.
Moving 60∘60^\circ East from 20∘W20^\circ\text{W} gives 40∘E40^\circ\text{E}.
Because Town B has a later time, it lies to the East. Subtracting 20∘20^\circ reaches the Prime Meridian (0∘0^\circ), leaving 40∘40^\circ in the Eastern Hemisphere.

Key Concept

Calculating Longitude from Local Solar Time Differences Across Meridians
Estimated Time:1m 30s
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Topics

Latitude, Longitude, and Time Calculations

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