Time zones and time differences (QCE General Mathematics Unit 3)

Syllabus dot point

“Understand the meaning of Greenwich Mean Time (GMT), the International Date Line and Coordinated Universal Time (UTC), understand the link between longitude and time, determine the number of degrees of longitude for a given time difference, calculate time differences between two places on Earth, and solve practical problems involving time zones, making allowances for daylight saving where necessary”

14 min readUpdated 23 Sep 2026

Quick answer

The Earth turns 15° of longitude per hour (1° is 4 minutes), so a longitude difference divided by 15 gives the time difference, and the place further east is ahead. Add longitudes across the prime meridian and subtract them on the same side. With time zones, subtract the UTC offsets, adding 1 hour to a place's offset during daylight saving (Queensland does not use it). Crossing the International Date Line westward moves the date forward a day. For flights, add the flight time in one zone, then convert, and give the time, day and date.

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What this dot point is asking
The answer
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What this dot point is asking

Because the Earth turns, different places see the Sun at different times, and their clocks show different times. The QCAA General Mathematics 2025 syllabus (Unit 3, Topic 5, Earth geometry and time zones, "Time zones") asks you to

understand the meaning of Greenwich Mean Time (GMT), the International Date Line and Coordinated Universal Time (UTC),
understand the link between longitude and time,
determine the number of degrees of longitude for a given time difference,
calculate time differences between two places on Earth, and
solve practical problems involving time zones (phone calls, broadcasting events, travelling, itineraries), making allowances for daylight saving where necessary.

Latitude, longitude and distances on the Earth are covered on their own page.

The answer

GMT, UTC and the International Date Line

Greenwich Mean Time (GMT) is the mean solar time at the prime meridian (0° longitude), which passes through Greenwich in London.
Coordinated Universal Time (UTC) is the international time standard, kept by atomic clocks. Time zones are written as offsets from it: Queensland is UTC+10, a place 5 hours behind UTC is UTC−5. For calculations, GMT and UTC are treated as the same.
The International Date Line runs roughly along the 180° meridian (bending around some countries). Places just west of it are the furthest ahead in time and places just east of it are the furthest behind, so crossing it changes the date: travelling west across it, the date goes forward one day; travelling east, it goes back one day.

Longitude and time

The Earth rotates 360° in 24 hours, so

\frac{360°}{24 \text{ h}} = 15° \text{ per hour}, \qquad \frac{60 \text{ min}}{15°} = 4 \text{ minutes per degree}.

Places east of you see the Sun first, so their clocks are ahead; places west are behind.

Time difference from longitudes

Find the longitude difference: subtract if both places are on the same side of the prime meridian (both E or both W); add if they are on opposite sides.
Convert: time difference (hours) $=$ longitude difference $\div 15$ , or minutes $=$ longitude difference $\times 4$ .
Direction: the place further east is ahead.

For example, 153° E and 116° E differ by $153 - 116 = 37°$ , which is $37 \times 4 = 148$ minutes, or 2 h 28 min.

Degrees from a time difference

Reverse the conversion: degrees $=$ hours $\times 15$ . A time difference of 3 h 20 min is $3\frac{1}{3} \times 15 = 50°$ of longitude.

Standard time zones and UTC offsets

Clocks do not follow exact longitude time; countries use standard time zones, usually whole hours (sometimes half hours) from UTC. Queensland's standard time, UTC+10, is the local time of the 150° E meridian ( $10 \times 15 = 150$ ). With offsets:

\text{time difference} = \text{offset}_A - \text{offset}_B,

and the place with the larger offset is ahead. UTC+10 and UTC−8 differ by $10 - (-8) = 18$ hours.

Read each question carefully: "using longitude" means use 15° per hour; "time zones" or "UTC+..." means use the offsets.

Daylight saving

During daylight saving, clocks move forward 1 hour, so the UTC offset increases by 1. In Australia, Queensland, Western Australia and the Northern Territory do not use daylight saving, while New South Wales, the ACT, Victoria, Tasmania and South Australia do (from early October to early April). So in summer, Sydney is on UTC+11 and is 1 hour ahead of Brisbane; in winter they show the same time. Adelaide is 30 minutes behind Brisbane in winter (UTC+9:30) but 30 minutes ahead in summer (UTC+10:30).

Flights, calls and broadcasts

A reliable method:

Write both places' UTC offsets (adjusted for daylight saving if it applies on that date).
Do all the clock arithmetic in one place's time (usually the departure city): add the flight time there.
Convert the result to the other place's time with the offset difference.
State the time, day and date in the place asked for.

Key fact

15° of longitude $=$ 1 hour; 1° $=$ 4 minutes. Add longitudes on opposite sides of Greenwich, subtract on the same side. East is ahead. With UTC offsets, the difference is the difference of the offsets. Daylight saving adds 1 hour to the offset. Crossing the International Date Line westward adds a day; eastward subtracts a day. Do flight arithmetic in one time zone, then convert.

Worked examples: longitude, zones and travel

1. Longitude time with minutes

Town A is at 153° E and town B is at 116° E. When it is 12:00 noon in town A, what is the local (longitude) time in town B?

Difference: Same side: $153 - 116 = 37°$ .
Convert: $37 \times 4 = 148$ minutes $=$ 2 h 28 min.
Direction: B is west of A, so behind: 12:00 noon $-$ 2 h 28 min $=$ 9:32 am.

Marker's note: the standard time zones of two such cities may differ by a whole number of hours; this question asked for longitude time, so 2 h 28 min is correct here.

2. Degrees from a time difference

Two places have local times that differ by 5 hours 30 minutes. How far apart are they in longitude?

Convert. $5.5 \times 15 = 82.5°$ .

Answer. 82.5° of longitude.

3. Across the prime meridian

It is 2:00 am in town A (30° N, 90° W). Find the local time in town B (26° S, 120° E).

Difference. Opposite sides: $90 + 120 = 210°$ ; $210 \div 15 = 14$ hours.

Direction. B is east, so ahead: 2:00 am $+$ 14 h $=$ 4:00 pm the same day.

4. A broadcast

A football final kicks off at 7:30 pm Saturday in a city on UTC+1. When does it start in Brisbane (UTC+10)?

Difference. $10 - 1 = 9$ hours; Brisbane is ahead.

Answer. 7:30 pm Saturday $+$ 9 h $=$ 4:30 am Sunday, Brisbane time.

5. Daylight saving

At 11:00 am on a Wednesday in January, a Sydney office (UTC+10, plus 1 hour daylight saving) phones offices in Brisbane (UTC+10) and Perth (UTC+8). What time is it in each?

Sydney's offset in January: Daylight saving applies: UTC+11.
Brisbane: $11 - 10 = 1$ hour behind: 10:00 am.
Perth: $11 - 8 = 3$ hours behind: 8:00 am.

Marker's note: in July (no daylight saving), Brisbane would show the same time as Sydney, and Perth would be 2 hours behind.

6. A flight across the Date Line

A flight leaves Brisbane (UTC+10) at 11:00 am on Tuesday and takes 13 h 30 min to reach a city on UTC−8. Find the local arrival time.

Arrival in Brisbane time: 11:00 am Tuesday $+$ 13 h 30 min $=$ 12:30 am Wednesday.
Offset difference: $10 - (-8) = 18$ hours; the destination is behind.
Local arrival: 12:30 am Wednesday $-$ 18 h $=$ 6:30 am Tuesday.
Comment: Flying east across the Date Line, the traveller lands at an earlier clock time on the same calendar day as they departed.

Common traps

Using latitude: Local time depends only on longitude.
Subtracting longitudes on opposite sides of Greenwich: 90° W and 120° E are $90 + 120 = 210°$ apart.
Getting the direction wrong: East is ahead. Check with common sense: Perth's clocks are behind Brisbane's.
Dividing by 24: Divide degrees by 15 to get hours.
Forgetting daylight saving, or applying it to Queensland: Queensland does not use daylight saving. Check the date against the daylight saving period before using an offset.
Mixing zones in a flight problem: Add the flight time in one zone, then convert once.
Leaving out the day and date: Many questions ask for the time, day and date; a change of day earns (or loses) the mark.

Exam technique

Write down each place's longitude or UTC offset first, with daylight saving applied if relevant. Show the difference calculation ( $90 + 120 = 210°$ , $210 \div 15 = 14$ h, or $10 - (-8) = 18$ h) and state "east is ahead" or "west is behind" in words. For flights, lay the working out as a timeline in one zone, then convert. Give the final answer as time, day and date, with am or pm (or 24-hour time) and the place's name.

Note

The Sun rises in the east, so people to the east of you start their day before you do: their clocks are ahead. Because the Earth spins all the way round in 24 hours, every 15 degrees you go east puts you one hour ahead. That is why it is evening in Brisbane when it is morning in London. Daylight saving just moves some places' clocks forward an hour in summer, and the Date Line in the Pacific is where the calendar day changes over.

Exam-style questions

Questions in the style of QCAA exam questions on this dot point, each with a worked answer. They are written by ExamExplained unless tagged "Past paper"; the year shows the paper a question is modelled on.

Practice3 marks

If it is 2:00 am local time in town A (30 degrees N 90 degrees W), calculate the local time in town B (26 degrees S 120 degrees E).

Show worked answer →

Only longitude matters for local time; the latitudes are distractors.

Step 1: longitude difference (1 mark): A is 90° W and B is 120° E, on opposite sides of the prime meridian, so add: $90 + 120 = 210°$ .
Step 2: time difference (1 mark): $210 \div 15 = 14$ hours.
Step 3: direction (1 mark): B is east of A, so B is ahead: 2:00 am $+$ 14 hours $=$ 4:00 pm the same day in town B.

Practice4 marks

A conference is being held in Singapore (UTC +8). a) A conference attendee got a flight from Brisbane (UTC +10) at 10:30 am Brisbane time on Monday 7 December. If the flight from Brisbane to Singapore took 7 hours and 40 minutes, determine the time, day and date in Singapore when the flight lands. [2 marks] b) A conference attendee from Dubai (UTC +4) arrived in Singapore at 5 pm Singapore time on Monday 7 December. If the flight from Dubai to Singapore took 8 hours and 25 minutes, determine the time, day and date in Dubai when the flight departed. [2 marks]

Show worked answer →

a) (2 marks). Add the flight time in Brisbane time (1 mark): 10:30 am $+$ 7 h 40 min $=$ 6:10 pm Brisbane time. Singapore is $10 - 8 = 2$ hours behind Brisbane (1 mark): 6:10 pm $-$ 2 h $=$ 4:10 pm Monday 7 December in Singapore.

b) (2 marks). Work backwards in Singapore time (1 mark): 5:00 pm $-$ 8 h 25 min $=$ 8:35 am Singapore time. Dubai is $8 - 4 = 4$ hours behind Singapore (1 mark): 8:35 am $-$ 4 h $=$ 4:35 am Monday 7 December in Dubai.

Do the clock arithmetic in one time zone first, then convert; mixing the two steps is where errors creep in.

Practice7 marks

Your friend is on a cruise ship. As their ship departs from X to travel 1350 km due west to Tarawa, they message you: 'Local time 6:12 am Wednesday and enjoying the sunrise as our ship begins its trip to Tarawa'. On the map, X is in time zone GMT -12 and Tarawa is GMT +12 (the ship crosses the International Date Line), while Queensland is GMT +10. Assuming the ship travels at 50 km/h, determine the time in Queensland when you phone your friend as soon as they arrive in Tarawa.

Show worked answer →

Step 1: travel time (1 mark): $1350 \div 50 = 27$ hours.
Step 2: X to Tarawa (1 mark): $+12 - (-12) = 24$ , so Tarawa is 24 hours ahead of X.
Step 3: Queensland to Tarawa (1 mark): $+10 - (+12) = -2$ , so Queensland is 2 hours behind Tarawa.
Step 4: departure in Tarawa time (1 mark): 6:12 am Wednesday at X is 6:12 am Thursday in Tarawa.
Step 5: arrival in Tarawa time (1 mark): 6:12 am Thursday $+$ 27 h $=$ 9:12 am Friday.
Step 6: Queensland time (1 mark): 9:12 am Friday $-$ 2 h $=$ 7:12 am Friday.
Step 7: communicate (1 mark): You phone at 7:12 am Friday, Queensland time. Working in one zone (Tarawa) throughout keeps the date change across the International Date Line under control.

Original3 marks

It is 9:00 pm on Friday in town P (45° S, 150° E). Using longitude only, determine the local time and day in town Q (10° N, 75° W).

Show worked answer →

Longitude difference (1 mark): Opposite sides of the prime meridian: $150 + 75 = 225°$ .
Time difference (1 mark): $225 \div 15 = 15$ hours.
Direction (1 mark): Q is west of P, so Q is behind: 9:00 pm Friday $-$ 15 h $=$ 6:00 am Friday in town Q.

Original4 marks

Brisbane uses UTC+10 all year. Adelaide uses UTC+9:30, but during daylight saving (from early October to early April) it moves its clocks forward 1 hour. A weekly online meeting starts at 9:00 am Brisbane time. (a) What time does the meeting start in Adelaide in July? (b) What time does it start in Adelaide in January? (c) An Adelaide member says the meeting "moves" twice a year. Explain.

Show worked answer →

(a) In July Adelaide is on UTC+9:30, 30 minutes behind Brisbane: the meeting starts at 8:30 am in Adelaide. (1 mark)

(b) In January Adelaide is on daylight saving time, UTC+10:30, 30 minutes ahead of Brisbane: the meeting starts at 9:30 am in Adelaide. (1 mark)

(c) Brisbane does not change its clocks, but Adelaide moves forward 1 hour in October and back 1 hour in April. So the Adelaide start time jumps from 8:30 am to 9:30 am in October and back to 8:30 am in April. (2 marks)

Original4 marks

A flight leaves Brisbane (UTC+10) at 10:15 pm on Monday and flies 9 hours 50 minutes to Honolulu (UTC−10). (a) Find the arrival time in Brisbane time. (b) Find the local arrival time and day in Honolulu. (c) Explain why the traveller arrives on the "same day" they left.

Show worked answer →

(a) 10:15 pm Monday $+$ 9 h 50 min $=$ 8:05 am Tuesday, Brisbane time. (1 mark)

(b) Honolulu is $10 - (-10) = 20$ hours behind Brisbane (1 mark): 8:05 am Tuesday $-$ 20 h $=$ 12:05 pm Monday, Honolulu time. (1 mark)

(c) The flight crosses the International Date Line travelling east, so the date goes back one day. The 20-hour time difference is larger than the flight time, so the local arrival time is earlier on the calendar than the departure. (1 mark)

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation2 marks

Two places are 60° of longitude apart. (a) What is the time difference? (b) How many degrees of longitude correspond to a time difference of 5 hours 30 minutes?

Show worked solution →

(a) $60 \div 15 = 4$ hours. (1 mark)

(b) $5.5 \times 15 = 82.5°$ . (1 mark)

foundation2 marks

Town A is at 153° E and town B is at 116° E. Using longitude only, find the time difference in hours and minutes, and state which town is ahead.

Show worked solution →

Both are east, so subtract: $153 - 116 = 37°$ ; $37 \times 4 = 148$ minutes $=$ 2 h 28 min. (1 mark)

Town A is further east, so it is 2 h 28 min ahead. (1 mark)

foundation2 marks

Explain the difference between GMT and UTC, and what happens to the date when you cross the International Date Line travelling west.

Show worked solution →

GMT is the mean solar time at the prime meridian (0°) at Greenwich; UTC is the international time standard, kept by atomic clocks, that time zones are defined from as offsets such as UTC+10. For everyday calculations they are treated as the same. (1 mark)

Crossing the International Date Line travelling west, the date moves forward one day. (1 mark)

core2 marks

A football final starts at 7:30 pm on Saturday in a city on UTC+1. At what time and day does it start in Brisbane (UTC+10)?

Show worked solution →

Brisbane is $10 - 1 = 9$ hours ahead. (1 mark)

7:30 pm Saturday $+$ 9 h $=$ 4:30 am Sunday in Brisbane. (1 mark)

core2 marks

It is 11:00 am on Wednesday in Sydney during daylight saving (UTC+11). What time is it in Perth (UTC+8, no daylight saving)?

Show worked solution →

Perth is $11 - 8 = 3$ hours behind Sydney during daylight saving. (1 mark)

11:00 am $-$ 3 h $=$ 8:00 am Wednesday in Perth. (1 mark)

exam3 marks

A flight leaves Brisbane (UTC+10) at 11:00 am on Tuesday and flies 13 hours 30 minutes to a city on UTC−8. Find the local arrival time and day.

Show worked solution →

Arrival in Brisbane time: 11:00 am Tuesday $+$ 13 h 30 min $=$ 12:30 am Wednesday. (1 mark)

The destination is $10 - (-8) = 18$ hours behind Brisbane. (1 mark)

12:30 am Wednesday $-$ 18 h $=$ 6:30 am Tuesday, local time. The traveller lands earlier on the clock than they left. (1 mark)

exam3 marks

A student in Cairns (UTC+10) wants to call a friend in a city on UTC−5 between 6:00 pm and 9:00 pm the friend's time. Between what times should the student call, in Cairns time, and on which day relative to the friend?

Show worked solution →

Cairns is $10 - (-5) = 15$ hours ahead. (1 mark)

6:00 pm $+$ 15 h $=$ 9:00 am the next day; 9:00 pm $+$ 15 h $=$ 12:00 noon the next day. (1 mark)

The student should call between 9:00 am and 12:00 noon Cairns time, on the day after the friend's date. (1 mark)

Practise this

Sources & how we know this

General Mathematics General senior syllabus 2025 — QCAA