Practice Maths

← Earth Geometry and Time Zones › Time Zones

Time Zones

Key Terms

Earth rotates 360° in 24 hours → 15° of longitude = 1 hour
Moving east: time increases (add hours)
Moving west: time decreases (subtract hours)
The prime meridian (0°) is the reference: UTC/GMT
UTC+10 means 10 hours ahead of UTC (e.g. AEST — Queensland)
The International Date Line (IDL) is approximately at 180° — crossing it changes the date
Time zones don’t follow longitude exactly — they follow national/political boundaries
Time difference from longitude:
Time difference = longitude difference / 15 (hours)

Converting times:
Eastern location time = UTC + (longitude°E / 15)
Western location time = UTC − (longitude°W / 15)

Key times:
Brisbane (AEST): UTC+10
London (GMT/BST): UTC+0 (or +1 in summer)
New York (EST): UTC−5
Worked Example: When it is 9:00 am Monday in Brisbane (UTC+10), what time and day is it in London (UTC+0)?

Difference: 10 hours ahead of UTC → London is 10 hours behind Brisbane.
London time = 9:00 am − 10 hours = 11:00 pm Sunday
Hot Tip: When subtracting hours takes you before midnight (e.g. 2:00 am − 5 hours), go back one day: 2:00 am − 5h = 9:00 pm the previous day. Always check whether the date changes.

Why Do Time Zones Exist?

The Earth rotates 360° in 24 hours, which means it rotates 15° per hour. Time zones are regions that observe the same standard time. Ideally, each 15° of longitude corresponds to one hour, but in practice, time zone boundaries follow national borders and other practical considerations.

UTC and Offsets

UTC (Coordinated Universal Time) is the world’s time standard, based at the prime meridian (0° longitude). Every time zone has an offset from UTC:

  • UTC+5:30 (India)
  • UTC+10 (Eastern Australia — AEST)
  • UTC+9:30 (South Australia — ACST)
  • UTC−8 (Pacific Standard Time, US west coast)

The International Date Line

The IDL runs approximately along the 180° meridian. If you cross it going east, you go back one day; going west, you go forward one day. This is why travel from Australia to the US involves “gaining” time while the return trip “loses” a day.

Calculating Time Differences

  1. Find the UTC offset for each location
  2. Subtract the UTC offsets to find the time difference
  3. Add or subtract to find local time
  4. Adjust for date change if needed
Strategy: Always convert to UTC first, then to the target time zone. This avoids confusion when crossing the date line or comparing zones on opposite sides of UTC.

Mastery Practice

See Answers ➔
  1. Fluency How many hours correspond to a longitude difference of 45°? Of 120°?
  2. Fluency A city is at 75°E longitude. What is its UTC offset (hours ahead of UTC)?
  3. Fluency It is 3:00 pm UTC. What is the local time in: (a) Brisbane (UTC+10)   (b) New York (UTC−5)?
  4. Fluency Brisbane is at UTC+10 and London is at UTC+0. When it is noon (12:00) in Brisbane, what is the time in London?
  5. Understanding A flight departs Sydney (UTC+10) at 8:00 am Monday and arrives in Los Angeles (UTC−8) after 14 hours of flying. What is the local time and day in Los Angeles on arrival?
  6. Understanding Perth (118°E) and Dubai (55°E) are both east of the prime meridian. What is the time difference between them? If it is 6:00 pm in Perth, what time is it in Dubai?
  7. Understanding London (UTC+0) wants to schedule a video call with Tokyo (UTC+9) and New York (UTC−5) so that it falls within business hours (9 am – 5 pm) for all three cities. Is this possible? Show your working.
  8. Understanding The city of Kathmandu, Nepal uses UTC+5:45 (a non-standard offset). If it is 10:00 am in Kathmandu, what is the time in London (UTC+0)?
  9. Problem Solving A business meeting is planned between Brisbane (UTC+10), London (UTC+0), and New York (UTC−5). The meeting must take place between 9:00 am and 6:00 pm local time for each participant. Find all possible start times (in UTC) that satisfy all three conditions, if any exist.
  10. Problem Solving An international flight departs Tokyo (UTC+9) at 11:30 pm Thursday and lands in Los Angeles (UTC−8) after 10 hours 45 minutes.
    • (a) What UTC time does the plane depart?
    • (b) What UTC time does it arrive?
    • (c) What is the local Los Angeles time and day on arrival?

View Full Worked Solutions →