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Difficulty: Very hardThe Earth as a Planet and Earth Movements

An aircraft departs from Town X, located at longitude 120∘W120^\circ\text{W}, at 4:00 a.m. local time on Monday. The non-stop flight to Town Y, located at longitude 75∘E75^\circ\text{E}, takes exactly 14 hours. What is the local time and day at Town Y when the aircraft lands?

  1. A
    5:00 a.m. on Monday
  2. B
    9:00 p.m. on Monday
  3. 7:00 a.m. on TuesdayAnswer
  4. D
    5:00 p.m. on Tuesday

Answer

7:00 a.m. on Tuesday
The correct answer is 7:00 a.m. on Tuesday. Town X (120∘W120^\circ\text{W}) and Town Y (75∘E75^\circ\text{E}) are separated by 195∘195^\circ of longitude (120∘+75∘120^\circ + 75^\circ). Dividing by 15∘15^\circ per hour yields a 13-hour time difference. Because Town Y is located east of Town X, local time at Town Y is 13 hours ahead of Town X. Thus, when the plane takes off at 4:00 a.m. Monday in Town X, the local time in Town Y is 5:00 p.m. Monday. Adding the 14-hour flight duration to 5:00 p.m. Monday results in 7:00 a.m. on Tuesday.

Step-by-Step Solution

1
Calculate total longitudinal difference between Town X and Town Y
Longitudinal difference = 120∘+75∘=195∘120^\circ + 75^\circ = 195^\circ
Since Town X is in the Western Hemisphere (120∘W120^\circ\text{W}) and Town Y is in the Eastern Hemisphere (75∘E75^\circ\text{E}), their angular distances from the Prime Meridian (0∘0^\circ) must be added together.
2
Convert the longitudinal difference into time difference
Time difference = 195∘15∘/hour=13 hours\frac{195^\circ}{15^\circ/\text{hour}} = 13\text{ hours}
The Earth rotates 360∘360^\circ in 24 hours, which corresponds to 15∘15^\circ per hour.
3
Determine the local time at Town Y at the exact moment of departure from Town X
Departure time at Town Y = 4:00 a.m. Monday + 13 hours = 5:00 p.m. (17:00) Monday
Places to the east gain time relative to places to the west ('East gain, West lose'). Town Y is east of Town X.
4
Add the flight duration to find the arrival time at Town Y
Arrival time at Town Y = 5:00 p.m. Monday + 14 hours = 7:00 a.m. Tuesday
Adding 14 hours to 5:00 p.m. (17:00) yields 31:00 hours. Subtracting 24 hours for a full day rollover gives 7:00 a.m. on the following day (Tuesday).

Key Concept

Calculating local time differences across Eastern and Western hemispheres combined with flight elapsed time and calendar day rollover.
Estimated Time:3m 0s
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Topics

The Earth as a Planet and Earth Movements

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