Coaching Centre
Time zones and UTC
Why 15 degrees of longitude is one hour, time differences from longitude, Coordinated Universal Time and time zones, the International Date Line, and flight arrival times.
When it is lunchtime in Parramatta, it is the middle of the night in London. If you have ever called family overseas, you have done this maths in your head. This section turns it into a method that works for any city and any flight, including the ones that "land before they take off".
Why $15°$ is one hour
The Earth spins once, $360°$, every $24$ hours. So in one hour it turns $\dfrac{360°}{24} = 15°$, and in one minute it turns $\dfrac{15°}{60} = \dfrac14°$. Flipping that around:
The Earth turns towards the east, so the sun rises in the east. Places further east see the sun first and are ahead in time. Places further west are behind.
Using longitude only, find the time difference between Brisbane ($153°$E) and Delhi ($77°$E).
Real clocks differ by $4$ h $30$ min, not $5$ h $4$ min. Clocks don't follow the sun exactly. Countries pick a time zone so that a whole region shares one clock. The longitude method gives the "sun time" difference, and exam questions say which one they want.
- Set Greenwich to $12{:}00$. Where is the sun? What sun time is it in Sydney?
- Move your longitude $15°$ east. How much does your sun time change? Try $30°$ and $45°$.
- Press Sydney, then drag Greenwich time until the sun is overhead in Sydney. What time is it in Greenwich?
UTC and time zones
Coordinated Universal Time (UTC) is the world's reference clock, kept by atomic clocks. It took over from Greenwich Mean Time (GMT) and matches it to within a second. Every time zone is written as UTC plus or minus a number of hours, called its offset.
| Place | Offset in January | Offset in July |
|---|---|---|
| Sydney | UTC+11 (daylight saving) | UTC+10 |
| Perth | UTC+8 | UTC+8 |
| Auckland | UTC+13 | UTC+12 |
| Tokyo | UTC+9 | UTC+9 |
| Delhi | UTC+5:30 | UTC+5:30 |
| London | UTC+0 | UTC+1 (summer time) |
| New York | UTC−5 | UTC−4 |
| Los Angeles | UTC−8 | UTC−7 |
To change a time from one city to another, find the difference between their offsets, then add it if you are going to a city that is ahead, or subtract if it is behind. Going through UTC is the safest way: subtract the first city's offset to get UTC, then add the second city's offset.
It is $3{:}00$ pm on Wednesday in Sydney in July (UTC+10). What time is it in London (UTC+1 in July)?
The International Date Line
Keep going east and the clocks keep going forward. Somewhere the day has to change, and that place is the International Date Line. It mostly follows the $180°$ meridian through the Pacific, with kinks so that island nations aren't split in two. Samoa even moved to the other side of the line in 2011, skipping Friday 30 December to line up its working week with Australia and New Zealand.
- Crossing the line travelling west (say Los Angeles to Sydney), the date jumps forward a day.
- Crossing east (Sydney to Los Angeles), the date goes back a day.
Flights
A flight takes the same number of hours whatever the clocks say. So convert the departure time to the arrival city's clock, then add the flight time. Or convert both through UTC.
A flight leaves Sydney at $9{:}30$ pm on Friday in January (UTC+11) and takes $13$ h $50$ min to reach Los Angeles (UTC−8). When does it land, in Los Angeles time?
- Check Example 3: Sydney to Los Angeles in January, leaving $21{:}30$, flight time $13$ h $50$ min.
- Switch the season to July. Why does the arrival time change by two hours even though the flight is the same?
- Plan Sydney to London leaving $21{:}15$ with a flight time of $22$ h $40$ min. Which day do you land?
- Find a pair of cities where a flight lands on the day before it left.
Your turn
A video call is set for $7{:}00$ pm Saturday in Sydney in January (UTC+11). What time and day is it for a cousin in Delhi (UTC+5:30)?
Show the working
UTC $= 19{:}00 - 11$ h $= 08{:}00$ Saturday. Delhi $= 08{:}00 + 5$ h $30$ min $= 13{:}30$, so $1{:}30$ pm Saturday.
Two places are $45°$ of longitude apart. Using longitude, how many hours apart are their times?
$45 \div 15 = 3$ hours.
How many minutes of time is $1°$ of longitude?
$1$ hour $= 15°$, so $1° = 60 \div 15 = 4$ minutes.
Using longitude, how many hours apart are places at $30°$E and $150°$E?
$150 - 30 = 120°$, and $120 \div 15 = 8$ hours.
It is $12{:}00$ UTC. What time is it in Sydney on UTC+10?
Add the offset: $12{:}00 + 10$ h $= 22{:}00$.
It is $8{:}00$ pm in Tokyo (UTC+9). What time is it in London in January (UTC+0)?
UTC $= 20{:}00 - 9$ h $= 11{:}00$. London is on UTC+0, so it is $11{:}00$ am.
In January Sydney is on UTC+11 and New York is on UTC−5. How many hours ahead is Sydney?
$11 - (-5) = 16$ hours.
A plane flies west from Los Angeles to Sydney, crossing the International Date Line. The date:
Travelling west across the line, the date jumps forward a day. That is why you "lose" a day flying to Australia from the USA.
Using longitude only, it is noon at Greenwich. What is the sun time at $60°$W?
$60 \div 15 = 4$ hours. West is behind, so $12{:}00 - 4$ h $= 08{:}00$.
Exam style: A flight leaves Perth (UTC+8) at $23{:}40$ on Monday and lands in Singapore (UTC+8) after $5$ h $20$ min. When does it land, local time?
Both cities use the same offset, so just add the flight time: $23{:}40 + 5$ h $20$ min $= 05{:}00$ on Tuesday.
Exam style: A flight leaves Sydney (UTC+11) at $9{:}30$ pm on Friday and takes $13$ h $50$ min to reach Los Angeles (UTC−8). When does it land, local time?
UTC departure $= 21{:}30 - 11 = 10{:}30$ Friday. Add $13$ h $50$ min: $00{:}20$ UTC Saturday. Los Angeles $= 00{:}20 - 8$ h $= 16{:}20$ Friday.