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Answer :
Sure, let's break down the solution step by step:
### (a) Arrival Time in Durban
1. Departure Time in Durban's Local Time:
- When Jerry leaves Melbourne, the time in Durban is 14:34 (2:34 PM) on Wednesday.
2. Flight Duration:
- The flight duration is 12 hours and 55 minutes.
3. Calculate Arrival Time:
- Start from 14:34 and add 12 hours and 55 minutes to find the arrival time in Durban.
Adding the hours and minutes:
- Start with 14:34, add 12 hours to get 26:34.
- Convert 26:34 into regular time by subtracting 24 hours from the hours part: 26:34 becomes 02:34.
- Adding the minutes: 34 + 55 equals 89 minutes. Since there's more than 60 minutes, convert it:
- This means 1 hour and 29 minutes.
- Add the extra hour to the current hour: 02:34 becomes 03:34.
- After adjusting with the extra minutes, we get 03:29.
Arrival Time in Durban: 03:29 AM on the next day, which is Thursday.
### (b) Arrival Time in Melbourne
1. Calculate Time Offset from Durban to Melbourne:
- The time difference between Durban and Melbourne is 9 hours and 36 minutes ahead.
2. Calculate Arrival Time in Melbourne:
- The calculated arrival time in Durban is 03:29 on Thursday. To find out what time it is in Melbourne, add the time difference to this.
3. Add the Time Offset:
- Start from 03:29 and add 9 hours and 36 minutes.
- Add the hours: 03 + 9 = 12 hours.
- Add the minutes: 29 + 36 = 65 minutes.
- 65 minutes is 1 hour and 5 minutes.
- Combine these adjustments to get 13:05 (1:05 PM).
Day Calculation:
- Since the time conversion does not shift the day back to Wednesday due to the large offset, it remains Thursday.
Arrival Time in Melbourne: 13:05 (1:05 PM) on Thursday.
### (c) Calculate the Longitude for Melbourne
1. Understanding the Problem:
- Durban is at [tex]\(31^{\circ}\)[/tex] East. We consider the time difference between Durban and Melbourne.
2. Calculate Time Difference:
- If Durban is 9 hours and 36 minutes (which is 9.6 hours) ahead, calculate longitude difference knowing every 1-hour difference equals 15 degrees of longitude.
3. Compute Melbourne’s Longitude:
- Longitude difference: [tex]\(9.6 \times 15 = 144\)[/tex] degrees.
- Since Durban is east and Melbourne’s local time is ahead, Melbourne should be 144 degrees East.
Melbourne’s Longitude: Approximately [tex]\(144^{\circ}\)[/tex] East.
This breakdown should help understand how the calculations were derived without requiring additional code or complex formulas.
### (a) Arrival Time in Durban
1. Departure Time in Durban's Local Time:
- When Jerry leaves Melbourne, the time in Durban is 14:34 (2:34 PM) on Wednesday.
2. Flight Duration:
- The flight duration is 12 hours and 55 minutes.
3. Calculate Arrival Time:
- Start from 14:34 and add 12 hours and 55 minutes to find the arrival time in Durban.
Adding the hours and minutes:
- Start with 14:34, add 12 hours to get 26:34.
- Convert 26:34 into regular time by subtracting 24 hours from the hours part: 26:34 becomes 02:34.
- Adding the minutes: 34 + 55 equals 89 minutes. Since there's more than 60 minutes, convert it:
- This means 1 hour and 29 minutes.
- Add the extra hour to the current hour: 02:34 becomes 03:34.
- After adjusting with the extra minutes, we get 03:29.
Arrival Time in Durban: 03:29 AM on the next day, which is Thursday.
### (b) Arrival Time in Melbourne
1. Calculate Time Offset from Durban to Melbourne:
- The time difference between Durban and Melbourne is 9 hours and 36 minutes ahead.
2. Calculate Arrival Time in Melbourne:
- The calculated arrival time in Durban is 03:29 on Thursday. To find out what time it is in Melbourne, add the time difference to this.
3. Add the Time Offset:
- Start from 03:29 and add 9 hours and 36 minutes.
- Add the hours: 03 + 9 = 12 hours.
- Add the minutes: 29 + 36 = 65 minutes.
- 65 minutes is 1 hour and 5 minutes.
- Combine these adjustments to get 13:05 (1:05 PM).
Day Calculation:
- Since the time conversion does not shift the day back to Wednesday due to the large offset, it remains Thursday.
Arrival Time in Melbourne: 13:05 (1:05 PM) on Thursday.
### (c) Calculate the Longitude for Melbourne
1. Understanding the Problem:
- Durban is at [tex]\(31^{\circ}\)[/tex] East. We consider the time difference between Durban and Melbourne.
2. Calculate Time Difference:
- If Durban is 9 hours and 36 minutes (which is 9.6 hours) ahead, calculate longitude difference knowing every 1-hour difference equals 15 degrees of longitude.
3. Compute Melbourne’s Longitude:
- Longitude difference: [tex]\(9.6 \times 15 = 144\)[/tex] degrees.
- Since Durban is east and Melbourne’s local time is ahead, Melbourne should be 144 degrees East.
Melbourne’s Longitude: Approximately [tex]\(144^{\circ}\)[/tex] East.
This breakdown should help understand how the calculations were derived without requiring additional code or complex formulas.
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