Practice Maths

Time Zones and Duration

Key Ideas

Key Terms

time zone
a region of the Earth that shares the same clock time, described by its offset from UTC.
UTC (Coordinated Universal Time)
the global time standard at 0° longitude. All other time zones are expressed as UTC + or − a number of hours.
UTC offset
the number of hours a time zone is ahead of (+) or behind (−) UTC. E.g. Brisbane = UTC+10; New York = UTC−5.
AEST / ACST / AWST
Australian time zones: AEST = UTC+10 (QLD); ACST = UTC+9:30 (SA, NT); AWST = UTC+8 (WA). Some states observe daylight saving (+1 hour in summer).
elapsed time
the actual duration between two events, measured in real hours — not affected by time zone changes on the clock.
crossing midnight
when a time conversion gives a result above 24:00 (next day) or below 0:00 (previous day), adjust the day label accordingly.

Converting Between Time Zones

  • Method 1 — via UTC: Convert the given time to UTC, then convert to the target zone.
  • Method 2 — direct offset: Find the difference between the two offsets and add or subtract.
Hot Tip “East is ahead, West is behind.” Moving east = add hours; moving west = subtract hours. When converting Brisbane (UTC+10) to London (UTC+0), you subtract 10 hours. Always check whether the answer crosses midnight and adjust the date accordingly.

Worked Example

Question: Brisbane is UTC+10. London is UTC+0. If it is 3:00 pm (1500) in Brisbane, what time is it in London?

Method — via UTC:
Step 1: Convert Brisbane time to UTC.
Brisbane = UTC+10, so UTC = Brisbane time − 10 h = 1500 − 1000 = 0500.

Step 2: Convert UTC to London time.
London = UTC+0, so London time = UTC = 0500.

Answer: It is 5:00 am in London.

Check using direct offset: Brisbane − London = 10 − 0 = 10 hours ahead. So London = 1500 − 1000 = 0500. ✓

What Are Time Zones?

The Earth rotates 360° every 24 hours, which means it turns 15° every hour. To keep things organised, the world is divided into time zones — regions that share the same clock time. The starting point is UTC (Coordinated Universal Time), which is the time at the 0° longitude line running through Greenwich, London. Every other time zone is described by how many hours it is ahead of or behind UTC.

For example, Brisbane is UTC+10, meaning Brisbane time is always 10 hours ahead of UTC. Tokyo is UTC+9, New York is UTC−5, and Los Angeles is UTC−8. The further east a city is, the higher (more positive) its offset; the further west, the more negative.

Converting Between Time Zones

There are two reliable methods for converting between time zones:

Method 1 — Via UTC (the safe way): First convert your starting time to UTC by subtracting its offset. Then add the destination's offset to get the local time there.

Example: It is 6:00 pm in Brisbane (UTC+10). What time is it in Dubai (UTC+4)?
Step 1: UTC = Brisbane time − 10 hours = 6:00 pm − 10 h = 8:00 am UTC.
Step 2: Dubai time = UTC + 4 hours = 8:00 am + 4 h = 12:00 pm (noon).

Method 2 — Direct offset difference: Find the difference between the two offsets and add or subtract. Brisbane is UTC+10, Dubai is UTC+4. Difference = 10 − 4 = 6. Brisbane is 6 hours ahead of Dubai, so Dubai time = Brisbane time − 6 hours = 6:00 pm − 6 h = 12:00 pm. Same answer!

Crossing Midnight — Watch the Date!

Some conversions land on a different calendar day. If the converted time goes past midnight (above 24:00) you are into the next day. If it goes below 0:00 (negative), you are into the previous day.

Example: It is 3:00 am Tuesday in Brisbane (UTC+10). What time is it in New York (UTC−5)?
Difference = +10 to −5 = 15 hours behind. New York = 3:00 am − 15 h = −12 hours, which is 12:00 pm Monday (the previous day).
Tip: convert to UTC first if you find direct subtraction confusing. UTC = 3:00 am − 10 h = 5:00 pm Monday. New York = 5:00 pm − 5 h = 12:00 pm Monday. Same result.

Australian Time Zones

Australia spans three main time zones (outside daylight saving):

  • AEST (Australian Eastern Standard Time): UTC+10 — Queensland, NSW, Victoria, Tasmania, ACT.
  • ACST (Australian Central Standard Time): UTC+9:30 — South Australia and Northern Territory.
  • AWST (Australian Western Standard Time): UTC+8 — Western Australia.

During summer, NSW, Victoria, SA, and Tasmania observe daylight saving, which adds 1 hour (e.g. Sydney becomes UTC+11 as AEDT). Queensland does not observe daylight saving — so the gap between Brisbane and Sydney changes depending on the season.

Calculating Travel Duration

When a flight crosses time zones, the clock time at the destination is not the same as the actual hours spent flying. To find the real flight duration, convert both departure and arrival times to UTC, then subtract.

Example: A flight departs Sydney (UTC+11) at 7:00 am and arrives in London (UTC+0) at 10:00 pm the same calendar day.
Departure in UTC = 7:00 am − 11 h = 8:00 pm (previous day). Arrival in UTC = 10:00 pm − 0 h = 10:00 pm.
Duration = from 8:00 pm to 10:00 pm = not the same day — from 8 pm (previous) to 10 pm = 26 hours.

Always use UTC to measure actual time elapsed — it is the only way to avoid being tricked by time zone changes.

Key tip: Remember the phrase "East is ahead, West is behind." Moving from one city to another further east means you add hours; moving west means you subtract. Always check whether your answer crosses midnight and adjust the day label accordingly. If you are ever unsure, convert everything to UTC first — it is your common reference point.

Mastery Practice

  1. Use the UTC offsets to convert each time. Fluency

    Reference: Brisbane = UTC+10, Sydney (AEDT) = UTC+11, Adelaide = UTC+10:30, Perth = UTC+8, Auckland = UTC+13, Tokyo = UTC+9, London = UTC+0, New York = UTC−5, Los Angeles = UTC−8, Dubai = UTC+4.

    1. It is 10:00 am in Brisbane. What time is it in London?
    2. It is 3:30 pm in Brisbane. What time is it in Perth?
    3. It is 8:00 am in London. What time is it in Brisbane?
    4. It is 6:00 pm in Sydney (AEDT). What time is it in New York?
    5. It is 11:00 am in Tokyo. What time is it in Brisbane?
    6. It is 2:00 pm in Dubai. What time is it in London?
    7. It is 9:00 am in Los Angeles. What time is it in Brisbane?
    8. It is 7:00 pm in Brisbane. What time is it in Auckland?

  2. Convert these times. Some answers cross midnight — state the day as “same day” or “previous day” or “next day” as appropriate. Fluency

    Use the same UTC reference table above.

    1. It is 2:00 am (Monday) in Brisbane. What time and day is it in London?
    2. It is 11:00 pm (Tuesday) in Brisbane. What time and day is it in Los Angeles?
    3. It is 1:00 am (Saturday) in London. What time and day is it in Brisbane?
    4. It is 10:00 pm (Friday) in New York. What time and day is it in Brisbane?
    5. It is 3:00 am (Wednesday) in Brisbane. What time and day is it in New York?
    6. It is 6:00 am (Thursday) in Auckland. What time and day is it in Brisbane?

  3. Convert between Australian time zones. Fluency

    Reference (no daylight saving): AEST = UTC+10 (QLD); ACST = UTC+9:30 (NT, SA); AWST = UTC+8 (WA).

    1. It is 10:00 am in Brisbane (AEST). What time is it in Perth (AWST)?
    2. It is 2:30 pm in Adelaide (ACST). What time is it in Brisbane (AEST)?
    3. It is 9:00 am in Perth (AWST). What time is it in Brisbane (AEST)?
    4. It is 6:00 pm in Brisbane (AEST). What time is it in Darwin/Adelaide (ACST)?
    5. It is 11:00 am in Darwin (ACST). What time is it in Perth (AWST)?
    6. It is 3:00 pm in Brisbane (AEST). What time is it in Adelaide (ACST)?
    7. A TV show airs at 7:30 pm in Brisbane (AEST). What time does it air in Perth?
    8. A meeting starts at 9:00 am in Perth (AWST). What time must someone in Adelaide (ACST) join?

  4. Calculate actual flight durations and arrival times. Remember: the clock time changes between zones, but duration is the real travel time. Understanding

    1. A flight departs Brisbane (UTC+10) at 9:00 am and arrives in Perth (UTC+8) at 11:30 am Perth time. What is the actual flight duration?
    2. A flight leaves Sydney (UTC+11, AEDT) at 7:00 am and takes 9 hours 30 minutes to reach Dubai (UTC+4). What is the local arrival time in Dubai?
    3. A flight from Brisbane (UTC+10) departs at 11:00 pm Monday and arrives in London (UTC+0) on Wednesday at 5:00 am. What is the actual flight duration?
    4. A direct flight from Los Angeles (UTC−8) departs at 10:30 pm and takes 15 hours to reach Brisbane (UTC+10). What is the local arrival time? On which day does it arrive (express as “next day,” “two days later,” etc.)?
    5. A flight from Auckland (UTC+13) departs at 5:45 pm and arrives in Brisbane (UTC+10) at 7:15 pm same day. What is the actual flight duration?
    6. A plane departs Tokyo (UTC+9) at 6:00 am Tuesday and arrives in Brisbane (UTC+10) at 2:30 pm Tuesday. What is the flight duration?

  5. Solve these scheduling and communication problems. Understanding

    1. A business in Brisbane (UTC+10) wants to hold a video call with partners in London (UTC+0) and New York (UTC−5). The Brisbane team is available 9:00 am – 5:00 pm, the London team is available 9:00 am – 5:00 pm, and the New York team is available 9:00 am – 5:00 pm. Find a time that works for all three teams (give the time in all three cities).
    2. Mia lives in Brisbane (UTC+10) and calls her friend in London (UTC+0) at 8:30 pm Brisbane time. The call lasts 45 minutes. What time does the call end in London?
    3. A live sporting event starts in Los Angeles at 11:00 am (UTC−8) on a Saturday. What time and day is it in Brisbane (UTC+10) when the event starts?
    4. A school in Brisbane (UTC+10) sends an email at 11:45 pm Monday to a school in New York (UTC−5). What time and day does the email arrive in New York?
    5. Tom is in Dubai (UTC+4) on a business trip. He needs to call his office in Brisbane (UTC+10) between 9:00 am and 5:00 pm Brisbane time. What is the window of Dubai time during which he can make the call?

  6. Extended time zone problems. Problem Solving

    1. A family is flying from Brisbane (UTC+10) to London (UTC+0) via Dubai (UTC+4). Their itinerary is:
      • Brisbane departs Monday 11:55 pm
      • Dubai arrives Tuesday 5:45 am (Dubai time); departs Tuesday 8:30 am (Dubai time)
      • London arrives Tuesday 1:10 pm (London time)
      1. How long is the Brisbane–Dubai leg (actual flight duration)?
      2. How long is the stopover in Dubai?
      3. How long is the Dubai–London leg?
      4. What is the total journey time from Brisbane to London (including stopover)?
    2. A TV network wants to broadcast a New Year countdown live from Sydney (UTC+11, AEDT) simultaneously to audiences in London and New York. Sydney’s New Year is at midnight 1 January.
      1. What time and date is the broadcast in London?
      2. What time and date is the broadcast in New York (UTC−5)?
      3. How many hours ahead of London is Sydney at this time?
    3. An online gaming tournament starts at 6:00 pm Saturday in Los Angeles (UTC−8). Players are joining from Brisbane (UTC+10), Tokyo (UTC+9), and London (UTC+0).
      1. What time and day does each city’s players join?
      2. One player in Brisbane says: “I have to stay up really late.” Is this correct? Explain.

  7. Use the time zone reference table to convert each time. Understanding

    City UTC offset Given time Local time in target city
    Brisbane (UTC+10)+103:00 pmTokyo (UTC+9) = ?
    London (UTC+0)+09:00 amNew York (UTC−5) = ?
    Dubai (UTC+4)+46:00 pmBrisbane (UTC+10) = ?
    Los Angeles (UTC−8)−811:00 pm FridayAuckland (UTC+13) = ?
    Sydney AEDT (UTC+11)+117:00 amLondon (UTC+0) = ?

    Show working for each conversion. Note if the answer falls on a different day.

  8. A traveller has the following flight itinerary. Complete the table by calculating each missing value. Understanding

    Leg Departure (local) Departure UTC Arrival (local) Arrival UTC Flight duration
    Brisbane → Singapore0800 (+10)?1230 (+8)??
    Singapore → London1700 (+8)?2200 (+0)??

  9. An international video conference is being planned. Use the information below to answer the questions. Problem Solving

    Team City UTC offset Available hours (local)
    Team ABrisbane+108 am – 5 pm
    Team BLondon+08 am – 5 pm
    Team CNew York−58 am – 5 pm
    1. Convert each team’s available hours to UTC. What time range (in UTC) do all three teams overlap?
    2. Is there any time that works for all three teams simultaneously? If yes, state the local time in each city. If not, suggest the best compromise.
    3. If the conference is scheduled at 10:00 am Brisbane time, what are the local times for London and New York? Are these reasonable working hours?

  10. Explain your reasoning clearly for each question. Problem Solving

    1. Can it ever be Tuesday in Brisbane and Monday in London at the same time? Explain using UTC offsets.
    2. A satellite circles the Earth every 90 minutes. It passes over Brisbane (UTC+10) at 2:00 pm. What is the UTC time of this pass? At what local time does it pass over New York (UTC−5) on the same orbit pass?
    3. Daylight saving moves clocks 1 hour forward. If Sydney (AEDT, UTC+11) is having daylight saving but Brisbane (AEST, UTC+10) is not, and it is 3:00 pm in Sydney, what time is it in Brisbane?
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