Time Zones and Duration — Solutions

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1. UTC offset conversions

   1. 10:00 am Brisbane → London: 1000 − 10 h = 0000 → 12:00 am (midnight) in London
   2. 3:30 pm Brisbane → Perth: 1530 − 2 h = 1330 → 1:30 pm in Perth
   3. 8:00 am London → Brisbane: 0800 + 10 h = 1800 → 6:00 pm in Brisbane
   4. 6:00 pm Sydney (AEDT, UTC+11) → New York (UTC−5): 1800 − 16 h = 0200 → 2:00 am in New York (same day)
   5. 11:00 am Tokyo (UTC+9) → Brisbane (UTC+10): 1100 + 1 h = 1200 → 12:00 pm (noon) in Brisbane
   6. 2:00 pm Dubai (UTC+4) → London (UTC+0): 1400 − 4 h = 1000 → 10:00 am in London
   7. 9:00 am Los Angeles (UTC−8) → Brisbane (UTC+10): 0900 + 18 h = 0300 next day → 3:00 am next day in Brisbane
   8. 7:00 pm Brisbane (UTC+10) → Auckland (UTC+13): 1900 + 3 h = 2200 → 10:00 pm in Auckland

2. Conversions crossing midnight

   1. 2:00 am Monday Brisbane → London: 0200 − 10 h = −0800 → Previous day (Sunday) 4:00 pm
   2. 11:00 pm Tuesday Brisbane → Los Angeles: 2300 − 18 h = 0500 → 5:00 am Tuesday (same day, since LA is 18 h behind)
   3. 1:00 am Saturday London → Brisbane: 0100 + 10 h = 1100 → 11:00 am Saturday
   4. 10:00 pm Friday New York (UTC−5) → Brisbane (UTC+10): 2200 + 15 h = 3700 → next day 1:00 pm → 1:00 pm Saturday
   5. 3:00 am Wednesday Brisbane → New York (UTC−5): 0300 − 15 h = −1200 → Previous day (Tuesday) 12:00 pm (noon)
   6. 6:00 am Thursday Auckland (UTC+13) → Brisbane (UTC+10): 0600 − 3 h = 0300 → 3:00 am Thursday

3. Australian time zones

   1. 10:00 am Brisbane (UTC+10) → Perth (UTC+8): 1000 − 2 h = 0800 → 8:00 am in Perth
   2. 2:30 pm Adelaide (UTC+9:30) → Brisbane (UTC+10): 1430 + 30 min = 1500 → 3:00 pm in Brisbane
   3. 9:00 am Perth (UTC+8) → Brisbane (UTC+10): 0900 + 2 h = 1100 → 11:00 am in Brisbane
   4. 6:00 pm Brisbane (UTC+10) → Adelaide (UTC+9:30): 1800 − 30 min = 1730 → 5:30 pm in Adelaide
   5. 11:00 am Darwin (UTC+9:30) → Perth (UTC+8): 1100 − 1 h 30 min = 0930 → 9:30 am in Perth
   6. 3:00 pm Brisbane (UTC+10) → Adelaide (UTC+9:30): 1500 − 30 min = 1430 → 2:30 pm in Adelaide
   7. 7:30 pm Brisbane → Perth: 1930 − 2 h = 1730 → 5:30 pm in Perth
   8. 9:00 am Perth → Adelaide: 0900 + 1 h 30 min = 1030 → 10:30 am in Adelaide

4. Flight durations

   1. Brisbane departs 9:00 am (UTC+10), arrives Perth 11:30 am (UTC+8): Arrival in UTC: 11:30 am − 8 h = 3:30 am UTC. Depart UTC: 9:00 am − 10 h = 11:00 pm previous day UTC. Duration = 3:30 am − 11:00 pm = 4 hours 30 minutes
   2. Sydney (UTC+11) departs 7:00 am, 9 h 30 min flight → Dubai (UTC+4): Depart UTC: 7:00 am − 11 h = 8:00 pm previous day. Arrive UTC: 8:00 pm + 9 h 30 min = 5:30 am. Dubai time: 5:30 am + 4 h = 9:30 am
   3. Brisbane Mon 11:00 pm → London Wed 5:00 am: Convert both to UTC. Depart: 11:00 pm − 10 h = 1:00 pm Mon UTC. Arrive: 5:00 am Wed − 0 h = 5:00 am Wed UTC. Duration = Mon 1:00 pm to Wed 5:00 am = 40 hours
   4. LA departs 10:30 pm (UTC−8), 15-hour flight → Brisbane (UTC+10): Depart UTC: 10:30 pm + 8 h = 6:30 am next day. Arrive UTC: 6:30 am + 15 h = 9:30 pm (next day). Brisbane time: 9:30 pm + 10 h = 7:30 am (two days after departure)
   5. Auckland departs 5:45 pm (UTC+13), arrives Brisbane 7:15 pm (UTC+10): Depart UTC: 5:45 pm − 13 h = 4:45 am. Arrive UTC: 7:15 pm − 10 h = 9:15 am. Duration = 4:45 am to 9:15 am = 4 hours 30 minutes
   6. Tokyo departs 6:00 am Tue (UTC+9), arrives Brisbane 2:30 pm Tue (UTC+10): Depart UTC: 6:00 am − 9 h = 9:00 pm Mon. Arrive UTC: 2:30 pm − 10 h = 4:30 am Tue. Duration = 9:00 pm Mon to 4:30 am Tue = 7 hours 30 minutes

5. Scheduling problems

   1. Video call across Brisbane, London, New York: When Brisbane is 9:00 am, London is 11:00 pm (previous day) — out of hours. When London is 9:00 am, Brisbane is 7:00 pm (in hours) and New York is 4:00 am (too early). Best window: Brisbane 5:00–6:00 pm = London 7:00–8:00 am (just in hours) = New York 2:00–3:00 pm — all within business hours. Example: Brisbane 5:00 pm, London 7:00 am, New York 2:00 pm.
   2. Mia calls at 8:30 pm Brisbane, call lasts 45 min → end time London: 8:30 pm Brisbane = 10:30 am London. Call ends: 10:30 am + 45 min = 11:15 am London
   3. LA sporting event 11:00 am Saturday (UTC−8) → Brisbane (UTC+10): 11:00 am + 18 h = 5:00 am Sunday → 5:00 am Sunday in Brisbane
   4. Email sent 11:45 pm Monday Brisbane (UTC+10) → New York (UTC−5): 2345 − 15 h = 0845 → 8:45 am Monday (same day) in New York
   5. Brisbane business hours 9:00 am – 5:00 pm (UTC+10) in Dubai time (UTC+4): 9:00 am Brisbane = 3:00 am Dubai; 5:00 pm Brisbane = 11:00 am Dubai. Call window: 3:00 am – 11:00 am Dubai time

6. Extended problems

   1. Brisbane–Dubai–London itinerary:
      1. Brisbane–Dubai duration: Depart Brisbane Mon 11:55 pm (UTC+10) = UTC Mon 1:55 pm. Arrive Dubai Tue 5:45 am (UTC+4) = UTC Tue 1:45 am. Duration: Mon 1:55 pm to Tue 1:45 am UTC = 11 hours 50 minutes
      2. Dubai stopover: Arrives 5:45 am, departs 8:30 am = 2 hours 45 minutes
      3. Dubai–London duration: Depart Tue 8:30 am (UTC+4) = UTC Tue 4:30 am. Arrive London Tue 1:10 pm (UTC+0) = UTC Tue 1:10 pm. Duration = 4:30 am to 1:10 pm = 8 hours 40 minutes
      4. Total Brisbane–London: 11 h 50 min + 2 h 45 min + 8 h 40 min = 23 hours 15 minutes
   2. Sydney New Year midnight broadcast:
      1. London: Sydney midnight (UTC+11) = 1:00 pm 31 December in London (UTC+0)
      2. New York (UTC−5): 1:00 pm 31 Dec London − 5 h = 8:00 am 31 December in New York
      3. Hours ahead: Sydney (UTC+11) is 11 hours ahead of London (UTC+0)
   3. Gaming tournament LA 6:00 pm Saturday (UTC−8):
      1. Brisbane: 1800 + 18 h = 3600 → 12:00 pm (noon) Sunday (next day). Tokyo: 1800 + 17 h = 3500 → 11:00 am Sunday. London: 1800 + 8 h = 0200 Sunday (2:00 am Sunday).
      2. Brisbane player claim: No — the event starts at 12:00 pm noon on Sunday in Brisbane, which is midday, not late at night. The Brisbane player does not need to stay up late.

7. World time zone reference table

   1. Brisbane 3:00 pm → Tokyo: 1500 − (10−9) = 1500 − 1 = 1400 (2:00 pm Tokyo)
   2. London 9:00 am → New York: 0900 − 5 = 0400 (4:00 am New York)
   3. Dubai 6:00 pm → Brisbane: 1800 + (10−4) = 1800 + 6 = 0000 next day (midnight Brisbane)
   4. LA 11:00 pm Friday → Auckland: 2300 + (13−(−8)) = 2300 + 21 = 44:00 → 44−24=20:00 = 8:00 pm Saturday in Auckland (next day)
   5. Sydney 7:00 am → London: 0700 − 11 = −4 = previous day 8:00 pm (2000 previous day London)

8. Flight itinerary table

   1. Brisbane → Singapore: Departure UTC = 0800−10h = 2200 (prev day). Arrival UTC = 1230−8h = 0430. Duration = 0430−2200(prev) = 6 h 30 min
   2. Singapore → London: Departure UTC = 1700−8h = 0900. Arrival UTC = 2200−0h = 2200. Duration = 2200−0900 = 13 hours

9. Conference scheduling

   1. UTC availability: Brisbane (UTC+10): 8am–5pm local = 2200–0700 UTC. London (UTC+0): 0800–1700 UTC. New York (UTC−5): 1300–2200 UTC. Overlap of all three: 1300–1700 UTC (a 4-hour window).
   2. Yes: 1300–1700 UTC. In Brisbane: 11 pm–3 am (not ideal). In London: 1:00 pm–5:00 pm (good). In New York: 8:00 am–12:00 pm (good). Brisbane team would need to work late; best compromise is 1300 UTC = 11 pm Brisbane, 1 pm London, 8 am New York.
   3. 10:00 am Brisbane = 0000 UTC. London = 0000 (midnight — not reasonable). New York = 0000 − 5 = previous day 7:00 pm (reasonable for New York, but midnight for London is not reasonable).

10. Time zone reasoning

    1. Yes. Brisbane is UTC+10, London is UTC+0, a difference of 10 hours. When it is 12:01 am Tuesday in Brisbane, UTC = 2:01 pm Monday. London is at UTC+0 so it is 2:01 pm Monday. So yes, Brisbane can be Tuesday while London is still Monday.
    2. UTC time = 1400 − 10 = 0400 UTC. New York local = 0400 − 5 = 2300 (11:00 pm). Same day if the pass is on a continuous single orbit cycle at the same moment — yes it is the same absolute UTC moment.
    3. Sydney AEDT = UTC+11; Brisbane AEST = UTC+10. Difference = 1 hour. Sydney 3:00 pm − 1 hour = 2:00 pm Brisbane.