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Question

Difficulty: MediumLatitude, Longitude, and Time Calculations

A solar power monitoring station at Site K, located at longitude 24∘W24^\circ\text{W}, records local solar noon (12:00 PM12:00\text{ PM}). At the exact same instant, a remote telecommunication hub at Site M records its local solar time as 05:20 PM05:20\text{ PM}. What is the longitude of Site M in degrees East?

Answer: 56 °E

Answer

The longitude of Site M is 56∘E56^\circ\text{E}.
The time difference between Site K (12:00 PM12:00\text{ PM}) and Site M (05:20 PM05:20\text{ PM}) is 5 hours 20 minutes5\text{ hours } 20\text{ minutes}. Converting time to longitude (15∘15^\circ per hour and 1∘1^\circ per 4 minutes4\text{ minutes}) yields an angular distance of 80∘80^\circ. Since Site M is ahead in time, it is located east of Site K. Subtracting 24∘24^\circ from 80∘80^\circ accounts for the distance to the Prime Meridian (0∘0^\circ), leaving 56∘56^\circ in the Eastern Hemisphere (56∘E56^\circ\text{E}).

Step-by-Step Solution

1
Calculate the time difference between the two locations.
Time difference = 17:20−12:00=5 hours 20 minutes17:20 - 12:00 = 5\text{ hours } 20\text{ minutes} (5.333 hours5.333\text{ hours}).
Differences in local solar time directly reflect differences in longitude.
2
Convert the time difference into angular degrees of longitude using the rate of 15∘15^\circ per hour (1∘1^\circ per 4 minutes4\text{ minutes}).
Angular distance = (5 hours×15∘/hr)+(20 min÷4 min/∘)=75∘+5∘=80∘(5\text{ hours} \times 15^\circ/\text{hr}) + (20\text{ min} \div 4\text{ min}/^\circ) = 75^\circ + 5^\circ = 80^\circ.
The Earth completes a 360∘360^\circ rotation in 24 hours.
3
Determine the direction of displacement and find the longitude of Site M.
Longitude of Site M = 80∘−24∘W=56∘E80^\circ - 24^\circ\text{W} = 56^\circ\text{E}.
Site M is ahead in time, so it lies to the east of Site K (24∘W24^\circ\text{W}). Traversing 80∘80^\circ eastward takes 24∘24^\circ to reach the Prime Meridian (0∘0^\circ) and the remaining 56∘56^\circ into the Eastern Hemisphere.

Key Concept

Calculating longitude across meridians from local solar time differences
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Topics

Latitude, Longitude, and Time Calculations

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