Examkin

Question

Difficulty: HardLatitude, Longitude, and Time Calculations

An airplane departs from Town X, located at longitude 45∘E45^\circ\text{E}, at 08:30 local time on Tuesday, bound for Town Y, located at longitude 75∘W75^\circ\text{W}. If the total flight duration is 10 hours, what is the local time and day of arrival at Town Y?

  1. 10:30 AM on TuesdayAnswer
  2. B
    02:30 AM on Wednesday
  3. C
    04:30 PM on Tuesday
  4. D
    12:30 AM on Tuesday

Answer

10:30 AM on Tuesday
The correct arrival time is 10:30 AM on Tuesday. Because Town X (45∘E45^\circ\text{E}) and Town Y (75∘W75^\circ\text{W}) are in different hemispheres, their longitudinal distance is 45∘+75∘=120∘45^\circ + 75^\circ = 120^\circ. Dividing by 15∘15^\circ per hour gives an 8-hour time difference. Since Town Y lies west of Town X, time is subtracted, making the local time at Town Y at the moment of departure 00:30 (12:30 AM) on Tuesday. Adding the 10-hour flight time results in arrival at 10:30 AM on Tuesday.

Step-by-Step Solution

1
Calculate total longitudinal difference between Town X (45∘E45^\circ\text{E}) and Town Y (75∘W75^\circ\text{W}).
45∘+75∘=120∘45^\circ + 75^\circ = 120^\circ longitudinal difference.
Locations in opposite hemispheres (East and West) require adding longitudes to find total angular separation.
2
Convert longitudinal difference into time difference using 15∘=1 hour15^\circ = 1\text{ hour}.
120∘15∘=8 hours\frac{120^\circ}{15^\circ} = 8\text{ hours} time difference.
Earth rotates 360∘360^\circ in 24 hours, which equals 15∘15^\circ per hour.
3
Determine local departure time at Town Y.
08:30−8 hours=00:30 (12:30 AM) on Tuesday08:30 - 8\text{ hours} = 00:30\text{ (12:30 AM) on Tuesday}.
Town Y is west of Town X, so local time is behind (subtract time when moving west).
4
Add the flight duration to the local departure time at Town Y.
00:30+10 hours=10:30 AM on Tuesday00:30 + 10\text{ hours} = 10:30\text{ AM on Tuesday}.
Elapsed flight time moves local arrival time forward by 10 hours.

Key Concept

Longitude and local time adjustment across meridians and flight duration
Estimated Time:2m 0s
Rate this question

Topics

Latitude, Longitude, and Time Calculations

More questions from this topic