Time & time zones - Year 8 Mathematics

What you will learn

convert between 12- and 24-hour time,
calculate durations across noon and midnight,
use standard time zone offsets (UTC) to find local time elsewhere,
plan travel and meetings that span multiple time zones,
account for daylight saving when it is relevant.

1. 12-hour vs 24-hour time

12-hour time uses a.m./p.m.; 24-hour time uses hours $00$ - $23$ .

12-hour	24-hour
$12$ midnight	$00{:}00$
$6$ a.m.	$06{:}00$
$12$ noon	$12{:}00$
$3{:}30$ p.m.	$15{:}30$
$11{:}45$ p.m.	$23{:}45$

For p.m. hours (1 through 11 p.m.), add $12$ to get the 24-hour form.

2. Duration across hours

Break the time span at each hour boundary (or at noon/midnight).

Worked example 1 Duration across midnight

A night shift starts at $22{:}15$ and ends at $06{:}40$ the next day. How long is the shift?

From $22{:}15$ to $24{:}00$ : $1$ h $45$ min.
From $00{:}00$ to $06{:}40$ : $6$ h $40$ min.
Total: $8$ h $25$ min.

3. Time zones

Time zones are expressed as an offset from UTC (Coordinated Universal Time).

Australian standard time zones (no daylight saving)

AEST - Australian Eastern Standard Time

$\text{UTC} + 10$ . Cities: Melbourne, Sydney, Brisbane, Hobart.

ACST - Australian Central Standard Time

$\text{UTC} + 9{:}30$ . Cities: Adelaide, Darwin.

AWST - Australian Western Standard Time

$\text{UTC} + 8$ . Cities: Perth.

To convert between two zones, subtract the offsets.

Worked example 2 Melbourne to Perth

It is $12{:}00$ noon in Melbourne (AEST, UTC+10). What time is it in Perth (AWST, UTC+8)?

Perth is $2$ hours behind Melbourne. $12{:}00 - 2{:}00 = 10{:}00$ a.m.

Worked example 3 Flight arrival time

A flight leaves Sydney (UTC+10) at $18{:}00$ and takes $8$ hours. It lands in Singapore (UTC+8). What is the local arrival time in Singapore?

Arrival in Sydney time: $18{:}00 + 8 = 02{:}00$ next day.
Convert to Singapore time: subtract $2$ hours → $00{:}00$ (midnight, next day).

4. Daylight saving (when it matters)

Most of south-eastern Australia observes daylight saving (AEDT/ACDT) from early October to early April, shifting the clock forward by $1$ hour. Perth, Brisbane, Darwin do not observe daylight saving.

Worked example 4 DST and AEDT

In January, Melbourne observes AEDT (UTC+11). Perth is still AWST (UTC+8). If it is $8{:}00$ a.m. in Melbourne in January, what time is it in Perth?

Perth is $3$ hours behind. $8{:}00 - 3{:}00 = 5{:}00$ a.m.

Practice: Year 8 core

Fluency

Convert and calculate

Convert $4{:}45$ p.m. to 24-hour time.
Convert $23{:}05$ to 12-hour time.
Duration from $9{:}15$ a.m. to $3{:}40$ p.m.
Duration from $22{:}50$ to $07{:}10$ next day.
Add $4$ h $25$ min to $11{:}20$ a.m.
Subtract $3$ h $40$ min from $02{:}15$ next day.

Fluency

Time zones (standard time)

It is $2{:}00$ p.m. in Sydney (AEST). What time in Perth (AWST)?
It is $9{:}30$ a.m. in Adelaide (ACST). What time in Brisbane (AEST)?
It is $10{:}00$ a.m. in Perth (AWST). What time in Melbourne (AEST)?
It is $12{:}00$ noon in London (UTC+0). What time in Melbourne (AEST)?
It is $6{:}00$ p.m. in New York (UTC $-5$ ). What time in Singapore (UTC+8)?

Reasoning

Explain and spot the mistake

Sam says “Melbourne is always $3$ hours ahead of Perth”. Is that always right? Explain.
Explain why a flight from Melbourne to Singapore sometimes lands on the same calendar day and sometimes the next day.
When travelling west, do you gain or lose time on arrival? Explain.
Write $12{:}00$ midnight as two equally valid 24-hour times. Which do most timetables prefer?

Problem solving

Real contexts

A video conference is scheduled for $9{:}00$ a.m. Melbourne time (AEST, April - no DST). What local time should the Perth participant join?
A flight leaves Singapore at $23{:}00$ local (UTC+8) and takes $7$ h $30$ min to Sydney (AEST, UTC+10). What is the local arrival time in Sydney?
A bus leaves Adelaide at $8{:}15$ a.m. (ACST) and arrives in Melbourne at $5{:}45$ p.m. (AEST). How long was the trip (in local times), accounting for the $30$ -minute zone difference?
A family flies Melbourne to Los Angeles (UTC $-8$ ) on a $14$ -hour flight that leaves at $10{:}00$ a.m. Melbourne AEDT (UTC+11) in January. What is the local arrival time in LA?

Answers

Answer key

Attempt the practice first. When you're ready to check, expand the answers below.

Show the full answer key

Year 8 core - answers

Fluency

Convert and calculate

$16{:}45$
$11{:}05$ p.m.
$6$ h $25$ min
$8$ h $20$ min
$3{:}45$ p.m.
$22{:}35$ (previous day)

Fluency

Time zones (standard time)

$12{:}00$ noon. Perth is $2$ h behind.
$10{:}00$ a.m. Brisbane is $30$ min ahead.
$12{:}00$ noon. Melbourne is $2$ h ahead.
$10{:}00$ p.m. ( $22{:}00$ ). Melbourne is $10$ h ahead.
$7{:}00$ a.m. next day. Singapore is $13$ h ahead of New York.

Reasoning

Explain and spot the mistake

Not always. In standard time it is $2$ h ahead; during daylight saving (October-April for Victoria) it is $3$ h ahead because Melbourne shifts to AEDT (UTC+11) while Perth stays on AWST (UTC+8).
A $7-9$ h westward flight that leaves in the morning can still land on the same day because local time “goes back” $2$ h, whereas a late-evening flight crosses the midnight boundary of the arrival zone.
You gain local time on arrival - your watch reads later locally than when you left (the clock runs ahead in local terms). Actually this depends on direction: flying west, local time is earlier, so you arrive at an earlier clock time than your travel hours suggest - effectively gaining hours in your day.
$00{:}00$ or $24{:}00$ both represent the midnight moment. Most timetables use $00{:}00$ as the start of the new day; $24{:}00$ is rare.

Problem solving

Real contexts

$7{:}00$ a.m. Perth time. Method: Perth is $2$ h behind Melbourne in April (both standard time).
$08{:}30$ AEST next day. Method: arrival in Singapore time $= 06{:}30$ ; add $2$ h for AEST.
$9$ h total. Method: Melbourne is $30$ min ahead of Adelaide. Bus leaves at $8{:}45$ Melbourne time; arrives $17{:}45$ ; duration $= 9$ h.
$6{:}00$ a.m. LA time same day. Method: arrival in Melbourne time $= 00{:}00$ next day. Melbourne AEDT is UTC+11; LA is UTC $-8$ ; LA is $19$ h behind Melbourne. $00{:}00$ next day $- 19$ h $= 05{:}00$ LA time. Actually: $24{:}00 - 19 = 05{:}00$ LA, same calendar day as arrival in Melbourne. Answer: $5{:}00$ a.m. LA local time on the day of departure.

Prefer paper? Print the answer key as a separate booklet: open print view ->