QLDGeneral MathematicsSyllabus dot point

Topic 3: Earth geometry - how do we relate longitude to local time and work out time differences between places?

Relate longitude to local time using the rule that the Earth turns 15 degrees of longitude per hour, calculate the time difference between two locations from their longitudes, apply the conventions of east being ahead and west being behind, and combine this with flight times

A focused answer to the QCE General Mathematics Unit 3 dot point on time zones. Covers the 15-degrees-per-hour rotation rule, calculating the time difference between two longitudes, the east-ahead west-behind convention, the International Date Line, and combining time zones with flight times, with arithmetic-verified worked examples for IA2 and the external assessment.

Generated by Claude Opus 4.76 min answerUpdated 2026-05-29

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking

QCAA wants you to turn longitude into local time. Because the Earth rotates once in $24$ hours, places to the east see the Sun earlier and run ahead in time, while places to the west run behind. You calculate the time difference between two locations from the gap in their longitudes, apply the east-ahead convention, and often combine this with a flight time to find an arrival time in local time. This is the second half of Unit 3 Topic 3 (Earth geometry) and appears in IA2 and the external assessment.

The answer

The rotation rule

The Earth rotates $360$ degrees in $24$ hours, so it turns

\frac{360}{24} = 15 \text{ degrees of longitude per hour}.

Equivalently, $15$ degrees corresponds to one hour, and $1$ degree corresponds to $4$ minutes of time ( $60 \div 15 = 4$ ). This rule converts any longitude gap into a time gap.

East is ahead, west is behind

The Sun rises in the east, so a place to the east experiences a later local time (it is ahead). A place to the west is behind. When moving east you add the time difference; when moving west you subtract it. This is the single rule that decides the sign of every answer.

Calculating a time difference

To find the difference between two locations, find the gap between their longitudes (add if on opposite sides of the prime meridian, subtract if on the same side), then divide by $15$ to convert degrees to hours.

\text{time difference (hours)} = \frac{\text{longitude difference (degrees)}}{15}.

If the answer is not a whole number, convert the leftover degrees at $4$ minutes per degree.

The International Date Line

Roughly along $180\degree$ longitude lies the International Date Line. Crossing it from east to west advances the calendar by one day; crossing from west to east goes back one day. In General Mathematics questions you usually only need to note that a long westward trip can land you on the next calendar day.

Combining with flight times

A typical question gives a departure local time, a flight duration, and the two longitudes. The method is: convert the longitude gap to a time difference, adjust the departure time to the destination's local time, then add the flight duration. Keep the time-zone adjustment and the flight time as separate steps.

Worked example

Arrival time across time zones

A plane leaves city A ( $30\degree$ E) at $9{:}00$ local time and flies for $5$ hours to city B ( $75\degree$ E). Find the local arrival time at city B.

Step 1: Longitude difference. Both are east of Greenwich, so subtract.

75\degree - 30\degree = 45\degree.

Step 2: Convert to a time difference. Divide by $15$ .

\frac{45}{15} = 3 \text{ hours}.

Verify: $15 \times 3 = 45$ . The cities are $3$ hours apart.

Step 3: Direction. City B is further east, so it is ahead of city A by $3$ hours. The departure moment in city B local time is

9{:}00 + 3 = 12{:}00.

Step 4: Add the flight time. The flight lasts $5$ hours.

12{:}00 + 5 = 17{:}00.

Verify: starting from $12{:}00$ , five hours later is $17{:}00$ . The plane arrives at $17{:}00$ local time in city B.

Common traps

Dividing by 24 instead of 15: The Earth turns $15$ degrees per hour, so divide the longitude gap by $15$ . Dividing by $24$ confuses the number of zones with the rotation rate.
Getting east and west the wrong way round: East is ahead in time. Travelling east you add hours; travelling west you subtract. Reversing this flips the answer.
Subtracting longitudes that straddle Greenwich: A point at $20\degree$ W and one at $30\degree$ E are $50$ degrees apart, found by adding. Only subtract when both are on the same side of the prime meridian.
Mixing the time-zone shift into the flight time: Adjust for the time zone first to get departure time in destination local time, then add the flight duration. Folding them together causes errors.
Forgetting the four-minutes-per-degree rule: If the longitude gap is not a multiple of $15$ , the leftover degrees convert at $4$ minutes each; dropping them loses precision.

Exam-style practice questions

Practice questions written in the style of QCAA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

2023 QCAA3 marksIf 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; latitude is a distractor.

Step 1 - longitude difference (1 mark). A is at 90 degrees W and B at 120 degrees E, on opposite sides of the prime meridian, so add: 90 + 120 = 210 degrees.

Step 2 - convert to a time difference (1 mark). The Earth turns 15 degrees per hour, so 210 / 15 = 14 hours.

Step 3 - apply direction and state (1 mark). B is east of A, and east is ahead, so B is 14 hours ahead: 2:00 am + 14 hours = 4:00 pm. The local time in town B is 4:00 pm (the same day from B's point of view).

The two traps are using latitude (irrelevant) and getting the direction backwards; going east across the globe puts you ahead in local time.

2021 QCAA4 marksA 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) Brisbane to Singapore (2 marks). Add the flight time first (1 mark): 10:30 am + 7 h 40 min = 6:10 pm Brisbane time. Then correct for the zone difference (1 mark): Singapore (UTC +8) is 2 hours behind Brisbane (UTC +10), so subtract 2 hours: 6:10 pm - 2 h = 4:10 pm. The flight lands at 4:10 pm on Monday 7 December in Singapore.

b) Dubai departure (2 marks). Work backwards from arrival. Subtract the flight time (1 mark): 5:00 pm - 8 h 25 min = 8:35 am Singapore time. Then correct for the zone difference (1 mark): Dubai (UTC +4) is 4 hours behind Singapore (UTC +8), so subtract 4 hours: 8:35 am - 4 h = 4:35 am. The flight departed Dubai at 4:35 am on Monday 7 December.

The reliable method is to do the clock arithmetic in one place first, then shift zones; mixing the two steps is where errors creep in.

2022 QCAA7 marksYour 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, 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): time = distance / speed = 1350 / 50 = 27 hours.

Step 2 - time difference X to Tarawa (1 mark): Tarawa GMT +12 minus X GMT -12 is +12 - (-12) = 24 hours, so Tarawa is 24 hours ahead of X.

Step 3 - time difference Queensland to Tarawa (1 mark): Queensland GMT +10 minus Tarawa GMT +12 is -2 hours, so Queensland is 2 hours behind Tarawa.

Step 4 - convert the message time to Tarawa time (1 mark): 6:12 am Wednesday at X is 6:12 am Wednesday + 24 hours = 6:12 am Thursday in Tarawa.

Step 5 - add the 27-hour voyage (1 mark): 6:12 am Thursday + 27 hours = 9:12 am Friday, the Tarawa arrival time.

Step 6 - convert to Queensland time (1 mark): Queensland is 2 hours behind Tarawa, so 9:12 am Friday - 2 hours = 7:12 am Friday.

Step 7 - communicate clearly (1 mark): you would phone at 7:12 am Friday Queensland time. The seventh mark rewards an organised solution that keeps the date changes straight across the International Date Line.