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Solutions — Time Zones

  1. Fluency Hours for 45° and 120° longitude differences.
    15° = 1 hour
    45° = 45/15 = 3 hours
    120° = 120/15 = 8 hours
  2. Fluency UTC offset for 75°E.
    UTC offset = 75/15 = UTC+5 (5 hours ahead of UTC)
  3. Fluency Local times when UTC = 3:00 pm.
    (a) Brisbane (UTC+10): 3:00 pm + 10h = 1:00 am (next day)
    (b) New York (UTC−5): 3:00 pm − 5h = 10:00 am (same day)
  4. Fluency Brisbane noon (UTC+10) → London time.
    Brisbane is 10 hours ahead of London.
    London time = 12:00 noon − 10h = 2:00 am
  5. Understanding Flight Sydney (UTC+10) 8:00 am Monday, 14 hours to LA (UTC−8).
    Departure UTC: 8:00 am − 10h = 10:00 pm Sunday (UTC)
    Arrival UTC: 10:00 pm Sunday + 14h = 12:00 noon Monday (UTC)
    LA local time: 12:00 noon − 8h = 4:00 am Monday

    The flight arrives at 4:00 am Monday Los Angeles time (same calendar day, though it departed Sunday night UTC).
  6. Understanding Perth (118°E) vs Dubai (55°E).
    Perth UTC offset: 118/15 ≈ 7.87 → uses UTC+8 (in practice)
    Dubai UTC offset: 55/15 ≈ 3.67 → uses UTC+4
    Time difference: 8 − 4 = 4 hours (Perth is 4 hours ahead)

    If it is 6:00 pm in Perth: 6:00 pm − 4h = 2:00 pm in Dubai
  7. Understanding London-Tokyo-New York video call in business hours.
    Business hours (9 am – 5 pm) expressed in UTC:
    London (UTC+0): 9:00 am – 5:00 pm UTC
    Tokyo (UTC+9): 9 am Tokyo = 12:00 am UTC; 5 pm Tokyo = 8:00 am UTC
    → Tokyo business hours: UTC 0:00 – 8:00
    New York (UTC−5): 9 am NY = 2:00 pm UTC; 5 pm NY = 10:00 pm UTC
    → NY business hours: UTC 14:00 – 22:00

    The UTC windows do not overlap (Tokyo: 0:00–8:00; London: 9:00–17:00; New York: 14:00–22:00). There is no time when all three are within business hours simultaneously.
  8. Understanding Kathmandu (UTC+5:45) 10:00 am → London time.
    London is 5h 45min behind Kathmandu.
    London time = 10:00 am − 5h 45min = 10:00 − 5:45 = 4:15 am
  9. Problem Solving Brisbane (UTC+10), London (UTC+0), New York (UTC−5), 9 am–6 pm local.
    Business hours in UTC:
    Brisbane 9 am – 6 pm = UTC 23:00 (prev day) – 8:00
    London 9 am – 6 pm = UTC 9:00 – 18:00
    New York 9 am – 6 pm = UTC 14:00 – 23:00

    Looking for UTC time that falls in all three windows:
    Brisbane and London overlap: UTC 9:00 – 8:00 AND UTC 9:00 – 18:00 → overlap is UTC 9:00 – 8:00 (wraps midnight, so effectively very late UTC)
    Wait — Brisbane 9 am = UTC 23:00 previous day; Brisbane 6 pm = UTC 8:00. So Brisbane window is UTC 23:00–08:00.
    London window is UTC 09:00–18:00.
    These do not overlap.

    There is no time when all three cities are simultaneously within 9 am – 6 pm. The 15-hour span between Brisbane and New York (UTC+10 vs UTC−5) makes it impossible.
  10. Problem Solving Tokyo (UTC+9) departs 11:30 pm Thursday, 10h 45min flight to LA (UTC−8).
    (a) Departure UTC:
    Tokyo 11:30 pm Thursday − 9h = 2:30 pm Thursday UTC

    (b) Arrival UTC:
    2:30 pm Thursday + 10h 45min = 1:15 am Friday UTC

    (c) LA local time:
    1:15 am Friday UTC − 8h = 1:15 am − 8h = 5:15 pm — go back one day? No:
    1:15 am − 8h: 1:15 am is only 1h 15min into Friday, so going back 8h means going to:
    1:15 am − 1:15 = midnight, then still need to subtract 6h 45min more → midnight − 6h 45min = 5:15 pm Thursday

    The flight lands at 5:15 pm Thursday local LA time. Despite departing on Thursday night in Tokyo, it arrives Thursday afternoon in LA — this is the famous phenomenon of “arriving before you leave” when flying east across the International Date Line.

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