Time Difference
A time difference is either the time between two clock times or the gap between the clocks in two places. This NSW Year 7 maths subtopic consolidates primary-school time skills and extends them to Australian time zones and overseas cities.
You will count on in easy jumps to find the time between two times, including overnight, use UTC offsets to tell which place is ahead or behind, allow for daylight saving, and keep track of the day when a flight crosses time zones. Video calling a grandparent in London from Sydney needs exactly this. This subtopic is part of Year 7 Ratios, Rates and Time.
Every question with a fully worked solution.
- Time Difference - Video - How To Add and Subtract Time in Hours and Minutes Watch
Theory
A time difference is the time between two times. Places in different time zones also have a time difference: at the same moment, their clocks show different times. This Year 7 maths page shows how to count on and back, and how to use UTC offsets to change a time from one zone to another.
Between two times, count on in easy jumps: to the next o’clock, then whole hours, then the minutes left. Overnight, jump to midnight first. To find an earlier time, count back the same way.
Time zones. Each zone is written as UTC (the world’s standard time) plus an offset. Australia has three standard time zones: the western zone (AWST, UTC\(+8\): WA), the central zone (ACST, UTC\(+9{:}30\): NT and SA) and the eastern zone (AEST, UTC\(+10\): QLD, NSW, ACT, VIC and TAS).
Step 1. Find the difference: the bigger offset minus the smaller offset.
Step 2. A place with a bigger offset is ahead: add. A place with a smaller offset is behind: take away. In Australia, the place further east is ahead.
Daylight saving time runs from the first Sunday in October to the first Sunday in April. NSW, the ACT, Victoria and Tasmania move their clocks forward \(1\) h, from AEST to AEDT (UTC\(+11\)), and SA moves from ACST to ACDT (UTC\(+10{:}30\)). WA, the NT and Queensland stay on standard time all year.
Overseas, go through UTC: subtract the first place’s offset to get UTC, then add the second place’s offset. Some places have negative offsets, such as UTC\(-5\): adding \(-5\) means taking away \(5\) h. Always track the day as well as the time.
Ahead or behind:
| Going to a place that is ... | do this |
|---|---|
| ahead (bigger offset, further east) | add the difference |
| behind (smaller offset, further west) | take away the difference |
Australian time zones (daylight saving runs from the first Sunday in October to the first Sunday in April):
| State or territory | Standard time | Daylight saving time |
|---|---|---|
| WA | AWST, UTC\(+8\) | none (stays UTC\(+8\)) |
| NT | ACST, UTC\(+9{:}30\) | none (stays UTC\(+9{:}30\)) |
| SA | ACST, UTC\(+9{:}30\) | ACDT, UTC\(+10{:}30\) |
| QLD | AEST, UTC\(+10\) | none (stays UTC\(+10\)) |
| NSW, ACT, VIC, TAS | AEST, UTC\(+10\) | AEDT, UTC\(+11\) |
How to find the time in another zone
- Write both UTC offsets (check the month for daylight saving).
- Find the difference: bigger offset minus smaller offset.
- Add if the other place is ahead; take away if it is behind.
- Check the day if you pass midnight.
With a flight
- Add the flight time in the departure zone first.
- Then change the arrival time to the other zone (or go through UTC).
(ii) What will the time be \(3\) hours \(10\) minutes after 7:25 am?
(i) 15:45 \(\to\) 16:00 is \(15\) min; 16:00 \(\to\) 21:00 is \(5\) h; 21:00 \(\to\) 21:20 is \(20\) min.
(ii) 7:25 am \(+ 3\) h \(=\) 10:25 am, then \(+ 10\) min.
| \(15 + 20\) | \(=\) | \(35\) |
(i) \(5\) h \(35\) min
(ii) 10:35 am
(ii) What was the time \(2\) h \(40\) min before 1:25 am?
(i) Jump to midnight first: \(20\) min to 10:00 pm, \(2\) h to midnight, \(6\) h to 6:00 am, then \(5\) min.
(ii) Count back: 1:25 am \(- 25\) min \(=\) 1:00 am; \(- 1\) h \(=\) midnight; \(- 1\) h \(15\) min \(=\) 10:45 pm.
| \(25 + 60 + 75\) | \(=\) | \(160\) |
(i) \(8\) h \(25\) min
(ii) 10:45 pm the day before
(i) a town in the western zone (UTC\(+8\))
(ii) a town in the central zone (UTC\(+9{:}30\))?
| \(10 - 8\) | \(=\) | \(2\) |
(i) The western zone is \(2\) h behind: 2:00 pm.
(ii) \(10\) h \(- 9\) h \(30\) min \(= 30\) min behind: 3:30 pm.
| \(11 - 10\) | \(=\) | \(1\) |
City B is \(1\) h behind: 7:20 pm. (In June, without daylight saving, both cities would show the same time.)
Add the flight time in city P time: 9:40 pm Tue \(+ 8\) h \(=\) 5:40 am Wed, then \(+ 25\) min \(=\) 6:05 am Wed. City Q is \(11 - 8 = 3\) h behind, so take away \(3\) h.
| \(11 - 8\) | \(=\) | \(3\) |
3:05 am on Wednesday, city Q time.
Go through UTC: 9:00 am Mon \(- 10\) h \(=\) 11:00 pm Sun (UTC). Then add \(-4\), which means take away \(4\) h.
| \(10 - (-4)\) | \(=\) | \(14\) |
7:00 pm on Sunday. The cities are \(10 - (-4) = 14\) h apart.
Common pitfalls
Frequently asked questions
How do you find the time difference between two times?
Count on from the earlier time to the next o’clock, then whole hours, then the minutes left.
What is a UTC offset?
How many hours a time zone is ahead of (or behind) UTC, the world’s standard time. UTC\(+10\) is \(10\) h ahead.
How many time zones does Australia have?
Three standard zones: UTC\(+8\) (WA), UTC\(+9{:}30\) (NT and SA) and UTC\(+10\) (QLD, NSW, ACT, VIC and TAS). In summer NSW, the ACT, VIC and TAS use UTC\(+11\) and SA uses UTC\(+10{:}30\).
Is a place to the east ahead or behind?
Ahead. A bigger offset means a later clock time.
How do you change a time to another country’s time?
Take away the first place’s offset to get UTC, then add the second place’s offset.