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Difficulty: Very hardLatitude, Longitude, and Time Calculations

An aircraft departs from City A located at longitude 35∘W35^\circ\text{W} at 08:45 AM08:45\text{ AM} local time on Tuesday for a non-stop flight to City B located at longitude 105∘E105^\circ\text{E}. If the total flight duration is 14 hours and 30 minutes, what is the local time and day of arrival at City B?

  1. 08:35 AM08:35\text{ AM} on WednesdayAnswer
  2. B
    01:55 PM01:55\text{ PM} on Tuesday
  3. C
    03:55 AM03:55\text{ AM} on Wednesday
  4. D
    08:35 PM08:35\text{ PM} on Tuesday

Answer

08:35 AM08:35\text{ AM} on Wednesday
The longitudinal difference between 35∘W35^\circ\text{W} and 105∘E105^\circ\text{E} is 140∘140^\circ, equivalent to a 9-hour 20-minute time difference. Since City B is east of City A, its time is ahead by 9 hours and 20 minutes, giving a local departure time at City B of 06:05 PM06:05\text{ PM} Tuesday. Adding the 14-hour 30-minute flight duration brings the time to 08:35 AM08:35\text{ AM} on Wednesday.

Step-by-Step Solution

1
Calculate the total longitudinal difference between City A (35∘W35^\circ\text{W}) and City B (105∘E105^\circ\text{E}).
Longitude difference=35∘+105∘=140∘\text{Longitude difference} = 35^\circ + 105^\circ = 140^\circ
Because the two places are in opposite hemispheres (West and East), their longitudinal values must be added.
2
Convert the longitudinal difference into a time difference.
140∘×4 minutes/degree=560 minutes=9 hours and 20 minutes140^\circ \times 4\text{ minutes/degree} = 560\text{ minutes} = 9\text{ hours and } 20\text{ minutes}
Earth rotates 1∘1^\circ every 4 minutes.
3
Determine the local time at City B when the flight departs from City A.
08:45 AM+9 hours 20 minutes=06:05 PM (or 18:05) on Tuesday08:45\text{ AM} + 9\text{ hours } 20\text{ minutes} = 06:05\text{ PM}\text{ (or } 18:05\text{)} \text{ on Tuesday}
Places to the East are ahead in time, so the time difference must be added to City A's departure time.
4
Add the flight duration to City B's departure time to find arrival time and day.
18:05+14 hours 30 minutes=32:35⇒08:35 AM on Wednesday18:05 + 14\text{ hours } 30\text{ minutes} = 32:35 \Rightarrow 08:35\text{ AM} \text{ on Wednesday}
32:3532:35 represents 8 hours and 35 minutes past midnight, which advances the calendar date by one day from Tuesday to Wednesday.

Key Concept

Calculation of time differences across eastern and western hemispheres considering flight duration and day change
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Topics

Latitude, Longitude, and Time Calculations

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