Open Math›Year 11›Mathematics Standard›Time and location›Time zones and UTC

Time zones and UTC

Convert between 12-hour and 24-hour time, work with Australian time zones and daylight saving, and solve multi-timezone problems using UTC offsets.

Worked examples

Converting between 12-hour and 24-hour time and finding elapsed time

Straightforward

Problem

A cinema session starts at

7{:}45\text{ pm}

and ends at

9{:}50\text{ pm}

. Write both times in 24-hour format and find the duration of the session in minutes.

Convert the start time from 12-hour to 24-hour format.

For pm times from

1{:}00\text{ pm}

onwards, add 12 to the hour.

7 + 12 = 19

, so

7{:}45\text{ pm} = 19{:}45

Convert the end time from 12-hour to 24-hour format.

9 + 12 = 21

, so

9{:}50\text{ pm} = 21{:}50

Calculate the elapsed time in minutes.

From

19{:}45

21{:}45

2

hours

= 120

minutes. From

21{:}45

21{:}50

5

minutes. Total duration

= 120 + 5 = 125

minutes.

Answer

Start:

19{:}45

; End:

21{:}50

; Duration:

125

minutes.

Converting between Australian time zones and expressing UTC offsets

Moderate

Problem

It is

4{:}30\text{ pm}

AEDT (UTC+11) in Sydney. Find the current time in Perth (AWST, UTC+8) and state the equivalent UTC time.

Convert Sydney AEDT to UTC by subtracting the UTC offset.

AEDT is UTC+11, so subtract 11 hours.

16{:}30 - 11 = 05{:}30

UTC.

Convert UTC to Perth time by adding Perth's UTC offset.

AWST is UTC+8, so add 8 hours.

05{:}30 + 8 = 13{:}30

. Perth time is

1{:}30\text{ pm}

(13:30).

State the UTC time and summarise.

The UTC time is

05{:}30

. Sydney (AEDT, UTC+11) is

3

hours ahead of Perth (AWST, UTC+8), since

11 - 8 = 3

Answer

UTC time:

05{:}30

; Perth time:

1{:}30\text{ pm}

(13:30).

Solving a multi-timezone flight problem using UTC

Challenging

Problem

A flight departs Auckland (NZST, UTC+12) at

9{:}00\text{ am}

on Saturday and takes 11 hours to reach Dubai (UTC+4). What is the local Dubai arrival time?

Convert the Auckland departure time to UTC.

NZST is UTC+12, so subtract 12 hours.

09{:}00 - 12 = -03{:}00

, which means

21{:}00

(9:00 pm) on Friday UTC. (Going back 12 hours from 9:00 am Saturday crosses midnight.)

Add the flight duration to find the arrival time in UTC.

21{:}00

Friday UTC

+ 11

hours

= 32{:}00 \to 08{:}00

Saturday UTC.

Convert the UTC arrival time to Dubai local time.

Dubai is UTC+4, so add 4 hours.

08{:}00 + 4 = 12{:}00

Saturday. The flight arrives at noon local time in Dubai.

Answer

The flight arrives at

12{:}00\text{ pm}

(noon) on Saturday in Dubai.

Practise

Q1·Straightforward

Convert

8{:}15\text{ pm}

to 24-hour time.

08:1518:1520:1521:15

Explanation

Add 12 to the hour:

8 + 12 = 20

. The minutes stay the same, so

8{:}15\text{ pm} = 20{:}15

Q2·Straightforward

Convert

13{:}40

(24-hour time) to 12-hour time.

1:40 am1:40 pm3:40 pm11:40 am

Explanation

Subtract 12 from the hour:

13 - 12 = 1

. The minutes stay the same, so

13{:}40 = 1{:}40\text{ pm}

Q3·Straightforward

A bus departs at

10{:}25

and arrives at

13{:}10

the same day. How many minutes does the journey take?

Explanation

From

10{:}25

13{:}25

3

hours

= 180

minutes. From

13{:}25

back to

13{:}10

-15

minutes. So the journey takes

180 - 15 = 165

minutes.

Q4·Straightforward

A film starts at

19{:}15

and ends at

21{:}50

. How many minutes long is the film?

Explanation

From

19{:}15

21{:}15

2

hours

= 120

minutes. From

21{:}15

21{:}50

35

minutes. Total:

120 + 35 = 155

minutes.

Q5·Moderate

Sydney uses AEST (UTC+10). When it is

3{:}00\text{ pm}

(15:00) in Sydney, what is the UTC time?

1:00 am5:00 am1:00 pm5:00 pm

Explanation

Sydney (AEST) is UTC+10, meaning Sydney is 10 hours ahead of UTC. Subtract 10 hours:

15{:}00 - 10 = 05{:}00

UTC

= 5{:}00\text{ am}

Q6·Moderate

Which UTC offset corresponds to AEDT (Australian Eastern Daylight Time), observed during summer in NSW and Victoria?

UTC+9UTC+10UTC+11UTC+12

Explanation

AEST (standard time) is UTC+10. During daylight saving, clocks move forward 1 hour, making AEDT =

\text{UTC}+10+1 = \text{UTC}+11

Q7·Moderate

Adelaide uses ACST (UTC+9:30). How many minutes ahead of UTC is Adelaide?

Explanation

ACST is UTC+9:30, meaning Adelaide is

9

hours and

30

minutes ahead of UTC. Converting:

9 \times 60 + 30 = 540 + 30 = 570

minutes.

Q8·Moderate

During daylight saving, Sydney observes AEDT (UTC+11) and Perth uses AWST (UTC+8). How many hours ahead of Perth is Sydney during this period?

Explanation

Sydney is UTC+11 and Perth is UTC+8. The difference is

11 - 8 = 3

hours. Sydney is

3

hours ahead of Perth.

Q9·Challenging

A flight departs Sydney (AEST, UTC+10) at

9{:}00\text{ pm}

on Monday and takes 8 hours to reach Singapore (SGT, UTC+8). At what hour does the flight arrive in Singapore? Give your answer as a whole number in 24-hour format (e.g. enter

14

for

2{:}00\text{ pm}

3

for

3{:}00\text{ am}

Explanation

Departure:

21{:}00

AEST (UTC+10)

\to

UTC:

21 - 10 = 11{:}00

UTC Monday. Add 8 hours:

11{:}00 + 8 = 19{:}00

UTC Monday. Convert to Singapore (UTC+8):

19 + 8 = 27{:}00 \to 03{:}00

Tuesday. The flight arrives at

3{:}00\text{ am}

(03:00) in Singapore.

Q10·Challenging

A live concert in New York (UTC

-

5) begins at

8{:}00\text{ pm}

on Saturday. At what hour (24-hour format, as a whole number) does the concert begin for a viewer in Melbourne observing AEDT (UTC+11)?

Explanation

New York (UTC

-

5):

20{:}00 \to

UTC:

20 + 5 = 01{:}00

Sunday. Melbourne (AEDT, UTC+11):

01{:}00 + 11 = 12{:}00

Sunday. The concert starts at

12{:}00

noon (12) on Sunday in Melbourne.

Q11·Challenging

A flight departs Tokyo (JST, UTC+9) at

11{:}00\text{ am}

on Wednesday and takes 10 hours to reach London (UTC+0). At what local London time does the flight arrive?

12:00 pm (noon)9:00 pm2:00 am8:00 pm

Explanation

Departure:

11{:}00

JST (UTC+9)

\to

UTC:

11 - 9 = 02{:}00

UTC Wednesday. Add 10 hours:

02{:}00 + 10 = 12{:}00

UTC. Since London is UTC+0, arrival is

12{:}00

noon local time on Wednesday.

Q12·Challenging

A webinar is scheduled for

10{:}00\text{ am}

UTC on Thursday. A participant in Dubai (UTC+4) wants to know their local start time. At what hour (24-hour format, as a whole number) does the webinar begin in Dubai?

Explanation

Dubai is UTC+4, meaning Dubai time

=

UTC time

+ 4

hours.

10{:}00 + 4 = 14{:}00

. The webinar begins at

14{:}00

(2:00 pm) in Dubai.