ACARA v9 CONTENT DESCRIPTION “solve problems involving duration, including using 12- and 24-hour time and time zones”
12-hour and 24-hour time
The 12-hour clock splits the day into two halves and labels them with am and pm. The am hours run from midnight up to noon, and the pm hours run from noon up to midnight, so the same reading, such as 8:20, comes around twice in one day. The 24-hour clock removes that doubt by counting the hours straight through from 00:00 to 23:59, with no am or pm needed. To turn a 12-hour time into a 24-hour time, leave the morning am times much as they are, and for a pm time after noon add 12 to the hour: 3:45 pm becomes 15:45, because 3 plus 12 is 15. Two readings are worth learning on their own, since they trip people up. Midnight, written 12 am, is 00:00 in 24-hour time, and noon, written 12 pm, is 12:00. Once those two anchors are clear, every other conversion is simply adding 12 or not.
12-hour and 24-hour time
For a pm time after noon, add 12 to the hour.
24-hour time runs 00:00 to 23:59; for pm times after noon, add 12 to the hour: 3:45 pm = 15:45.
Finding a duration
A duration is the amount of time that passes between a start time and an end time, and the safest way to find one is to count up in small steps rather than to subtract in a single go. The method is sometimes called bridging. Start at the earlier time and jump to the next whole hour, noting the minutes used. Then count on in whole hours to get close to the end time, and finish with the leftover minutes. Take the stretch from 9:40 am to 11:15 am. From 9:40 you step up 20 minutes to reach 10:00, then a full hour to reach 11:00, and finally 15 more minutes to reach 11:15. Adding the pieces gives 20 minutes plus 1 hour plus 15 minutes, which is 1 hour and 35 minutes in total. Counting up like this keeps the minutes and the hours apart, so it is harder to make a careless slip.
Finding a duration by bridging
Count up to the next hour, then on, then the spare minutes.
find a duration by counting up in steps to the next hour and on: 9:40 to 11:15 is 1 hour 35 minutes.
Durations across midday and midnight
Durations get harder to picture when they cross over noon or midnight, because the am and pm labels flip in the middle. The cleanest fix is to convert both the start and the end into 24-hour time first, and then bridge as before. Consider the time from 10:30 am to 1:15 pm. Written in 24-hour time these become 10:30 and 13:15, since 1:15 pm is 1 plus 12, or 13:15. Now bridge: from 10:30 it is 1 hour and 30 minutes up to 12:00, and then 1 hour and 15 minutes more up to 13:15. The two parts add to 2 hours and 45 minutes. Working in 24-hour time means the numbers always climb, so you never have to puzzle over whether the finish lands in the morning or the afternoon.
A duration across midday
Switch to 24-hour time, then bridge across noon.
crossing midday is easier in 24-hour time: 10:30 to 13:15 is 2 hours 45 minutes.
What a time zone is
The surface of the planet is divided into time zones, and each zone runs its clocks a whole number of hours away from a shared reference called UTC, short for Coordinated Universal Time. At any single instant every place shares the same moment, yet the local clock reading is different from zone to zone. Places to the east are ahead of UTC and read a later time, while places to the west are behind UTC and read an earlier time. Eastern Australia uses AEST, which is UTC plus 10, written UTC+10. Western Australia uses AWST, which is UTC plus 8, written UTC+8. So at the very same instant the clock in the east is two hours further on than the clock in the west, simply because the two zones sit at different offsets from UTC.
A time zone is an offset from UTC
One instant, two clock readings: Perth and Sydney.
a time zone is an offset from UTC; the same instant is 3:00 pm in Sydney (UTC+10) and 1:00 pm in Perth (UTC+8).
Converting between time zones
To convert a time from one zone into another, first work out the hour gap between the two zones by comparing their offsets. To move to a zone that is behind, subtract that many hours; to move to a zone that is ahead, add them. Suppose it is 3:00 pm in Sydney, which keeps AEST at UTC+10, and you want the time in Perth, which keeps AWST at UTC+8. The gap between UTC+10 and UTC+8 is two hours, and Perth is the one behind, so subtract two hours from 3:00 pm to get 1:00 pm in Perth. The same instant, two clock faces, one short subtraction. As an aside, some regions also shift their clocks forward for daylight saving in summer, which changes the offset for part of the year, but the worked examples here all use fixed standard offsets.
Converting between two zones
Use the hour gap: behind means subtract, ahead means add.
to convert, use the hour gap: Perth is 2 hours behind Sydney, so 3:00 pm in Sydney is 1:00 pm in Perth.
Why this matters
Time arithmetic quietly runs a great deal of daily life. You lean on it to catch a train or a bus, to work out how long a journey will take, to join an online call with someone in another city or another country, and to watch live sport beamed in from overseas. The practical skills are the same three you have just seen: converting between 12-hour and 24-hour time, finding a duration between two moments, and handling whole-hour offsets between zones. The two slips to guard against are forgetting to add 12 when writing a pm time in 24-hour form, and mixing up which zone is ahead and which is behind. Keep those straight and the rest is steady counting. This unit stays with clock time and whole-hour zone offsets; rates and other measures build on these ideas in a later unit.
Quick self-check
1. Write 3:45 pm in 24-hour time.
2. How long is it from 9:40 am to 11:15 am?
3. How long is it from 10:30 am to 1:15 pm?
4. AEST is UTC+10 and AWST is UTC+8. How far ahead is Sydney (AEST) of Perth (AWST)?
5. It is 3:00 pm in Sydney (AEST). What is the time in Perth (AWST), 2 hours behind?