Answer :
To determine the time difference between Juneau and Dubai, let's analyze the given time conversions in the table step by step:
1. Juneau to Oslo:
- When it is 10:00 AM in Juneau, it is 8:00 PM in Oslo.
- The time difference is [tex]\(8:00 \text{ PM} - 10:00 \text{ AM}\)[/tex].
- Converting everything to a 24-hour format:
- 10:00 AM is 10:00.
- 8:00 PM is 20:00.
- The difference is [tex]\(20 - 10 = 10\)[/tex] hours.
- Since Oslo is ahead, the time difference is [tex]\(-10\)[/tex] hours.
2. Oslo to Santiago:
- When it is 5:00 PM in Oslo, it is 11:00 AM the next day in Santiago.
- The time difference is [tex]\(11:00 \text{ AM next day} - 5:00 \text{ PM}\)[/tex].
- Converting everything to a 24-hour format:
- 5:00 PM is 17:00.
- 11:00 AM is 11:00.
- The difference is [tex]\(11 - 17 = -6\)[/tex] hours.
- Since Santiago is behind, the time difference is [tex]\(6\)[/tex] hours.
3. Santiago to Kuala Lumpur:
- When it is 3:00 AM in Santiago, it is 3:00 PM on the same day in Kuala Lumpur.
- The time difference is [tex]\(3:00 \text{ PM same day} - 3:00 \text{ AM}\)[/tex].
- Converting everything to a 24-hour format:
- 3:00 AM is 3:00.
- 3:00 PM is 15:00.
- The difference is [tex]\(15 - 3 = -12\)[/tex] hours.
- Since Kuala Lumpur is ahead, the time difference is [tex]\(-12\)[/tex] hours.
4. Kuala Lumpur to Dubai:
- When it is 2:00 AM in Kuala Lumpur, it is 10:00 PM the previous day in Dubai.
- The time difference is [tex]\(10:00 \text{ PM previous day} - 2:00 \text{ AM}\)[/tex].
- Converting everything to a 24-hour format:
- 2:00 AM is 2:00.
- 10:00 PM is 22:00 the previous day.
- The difference is [tex]\(22 - 2 = -20\)[/tex] hours.
- Since Dubai is behind, the time difference is [tex]\(-20\)[/tex] hours.
5. Total time difference from Juneau to Dubai:
- Summing up all the individual time differences:
[tex]\[ -10 \, \text{(Juneau to Oslo)} + 6 \, \text{(Oslo to Santiago)} + (-12 \, \text{(Santiago to Kuala Lumpur)}) + (-20 \, \text{(Kuala Lumpur to Dubai)}) \][/tex]
- [tex]\[ -10 + 6 - 12 - 20 \\ = -36 \][/tex]
- The total cumulative time difference is 36 hours, which means 36 hours forward or backward results in 12 hours difference due to 24-hour time format.
Therefore, the time difference between Juneau and Dubai is:
[tex]\[ \boxed{36 \equiv 12 \pmod{24}} \][/tex]
Thus, the correct answer is:
a. 12 hours
1. Juneau to Oslo:
- When it is 10:00 AM in Juneau, it is 8:00 PM in Oslo.
- The time difference is [tex]\(8:00 \text{ PM} - 10:00 \text{ AM}\)[/tex].
- Converting everything to a 24-hour format:
- 10:00 AM is 10:00.
- 8:00 PM is 20:00.
- The difference is [tex]\(20 - 10 = 10\)[/tex] hours.
- Since Oslo is ahead, the time difference is [tex]\(-10\)[/tex] hours.
2. Oslo to Santiago:
- When it is 5:00 PM in Oslo, it is 11:00 AM the next day in Santiago.
- The time difference is [tex]\(11:00 \text{ AM next day} - 5:00 \text{ PM}\)[/tex].
- Converting everything to a 24-hour format:
- 5:00 PM is 17:00.
- 11:00 AM is 11:00.
- The difference is [tex]\(11 - 17 = -6\)[/tex] hours.
- Since Santiago is behind, the time difference is [tex]\(6\)[/tex] hours.
3. Santiago to Kuala Lumpur:
- When it is 3:00 AM in Santiago, it is 3:00 PM on the same day in Kuala Lumpur.
- The time difference is [tex]\(3:00 \text{ PM same day} - 3:00 \text{ AM}\)[/tex].
- Converting everything to a 24-hour format:
- 3:00 AM is 3:00.
- 3:00 PM is 15:00.
- The difference is [tex]\(15 - 3 = -12\)[/tex] hours.
- Since Kuala Lumpur is ahead, the time difference is [tex]\(-12\)[/tex] hours.
4. Kuala Lumpur to Dubai:
- When it is 2:00 AM in Kuala Lumpur, it is 10:00 PM the previous day in Dubai.
- The time difference is [tex]\(10:00 \text{ PM previous day} - 2:00 \text{ AM}\)[/tex].
- Converting everything to a 24-hour format:
- 2:00 AM is 2:00.
- 10:00 PM is 22:00 the previous day.
- The difference is [tex]\(22 - 2 = -20\)[/tex] hours.
- Since Dubai is behind, the time difference is [tex]\(-20\)[/tex] hours.
5. Total time difference from Juneau to Dubai:
- Summing up all the individual time differences:
[tex]\[ -10 \, \text{(Juneau to Oslo)} + 6 \, \text{(Oslo to Santiago)} + (-12 \, \text{(Santiago to Kuala Lumpur)}) + (-20 \, \text{(Kuala Lumpur to Dubai)}) \][/tex]
- [tex]\[ -10 + 6 - 12 - 20 \\ = -36 \][/tex]
- The total cumulative time difference is 36 hours, which means 36 hours forward or backward results in 12 hours difference due to 24-hour time format.
Therefore, the time difference between Juneau and Dubai is:
[tex]\[ \boxed{36 \equiv 12 \pmod{24}} \][/tex]
Thus, the correct answer is:
a. 12 hours
