YEAR 8 · TIME AND TIME ZONES · 17 MIN

Time-zone differences

Convert local clock readings using given UTC offsets, including half-hour differences.

In this lesson

Use UTC as a common reference.
Find the difference between two given offsets.
Handle half-hour offsets without treating hours as base 100.

Before you start

Use 24-hour time.
Add and subtract hours and minutes.

01 / LEARN

Understand the idea.

Use a common reference

A UTC offset compares a local clock with one shared reference clock. UTC+8 is 8 hours ahead of UTC; UTC−5 is 5 hours behind. Undo the origin's offset to reach UTC, then apply the destination's offset.

Use the fixed offsets supplied for the question rather than assuming a city's seasonal rules. In UTC+9:30, the last part means 30 minutes. It is $9.5$ hours, not $9.30$ decimal hours.

\begin{aligned} destination time & = origin time \\ + destination offset \\ - origin offset \end{aligned}

Compare offsets first

Subtract the origin offset from the destination offset to find the clock change. From UTC+8 to UTC+9:30, add 1 hour 30 minutes. From UTC−5 to UTC+2, the gap is $2 - (- 5) = 7$ hours ahead.

A positive difference means add time; a negative difference means subtract it. After changing the hour, check whether the local day changes too. Reversing the same conversion should recover the original time and date.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A half-hour difference

At a town using UTC+8, the time is 14:20. What time is it simultaneously in a town using UTC+9:30?

Worked solution

1
Compare destination and origin offsets.
$9 h 30 min - 8 h = 1 h 30 min$
The larger destination offset puts its clock ahead.
2
Add the difference to the origin reading.
$14:20 + 1 h 30 min = 15:50$
The two clock readings describe the same instant.
3
Check by converting back.
$15:50 - 1 h 30 min = 14:20$
Reversing the offset change restores the given time.

Answer

15:50.

EXAMPLE 02

Across UTC

At a town using UTC−5, it is 08:40. Find the simultaneous time at UTC+2.

Worked solution

1
Find the signed offset change.
$2 - (- 5) = 7 h$
Moving from five hours behind UTC to two hours ahead crosses a seven-hour gap.
2
Move the clock seven hours ahead.
$08:40 + 7 h = 15:40$
The destination has the greater UTC offset.
3
Check the shared UTC instant.
$\begin{aligned} 08:40 + 5 h & = 13:40 UTC \\ 15:40 - 2 h & = 13:40 UTC \end{aligned}$
Both local readings must represent the same UTC time.

Answer

15:40.

03 / YOUR TURN

Try it yourself.

Check your understanding

A clock at UTC+3 shows 16:10. What does a clock at UTC+1 show?

Show answer & reasoning

14:10.

The change from UTC+3 to UTC+1 is $1 - 3 = - 2$ hours. Subtracting 2 hours from 16:10 gives 14:10.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

UTC+2 shows 09:15. Find the simultaneous time at UTC+5.
2 marks
UTC+9:30 shows 17:20. Find the simultaneous time at UTC+8.
2 marks
UTC−4 shows 11:35. Find the simultaneous time at UTC+1.
2 marks
UTC+10 shows 20:10. Find the simultaneous time at UTC−2.
2 marks
UTC+5:30 shows 13:45. Find UTC.
2 marks
A student converts 10:00 at UTC+8 to UTC+9:30 and gets 11:30. Reverse the conversion to check.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

UTC+2 shows 09:15. Find the simultaneous time at UTC+5.
2 marks
The destination is 3 h ahead.
12:15.
UTC+9:30 shows 17:20. Find the simultaneous time at UTC+8.
2 marks
Subtract 1 h 30 min.
15:50.
UTC−4 shows 11:35. Find the simultaneous time at UTC+1.
2 marks
The gap is $1 - (- 4) = 5$ h.
16:35.
UTC+10 shows 20:10. Find the simultaneous time at UTC−2.
2 marks
The destination is 12 h behind: $20:10 - 12 h = 08:10$ .
08:10.
UTC+5:30 shows 13:45. Find UTC.
2 marks
Subtract 5 h 30 min.
08:15.
A student converts 10:00 at UTC+8 to UTC+9:30 and gets 11:30. Reverse the conversion to check.
2 marks
The clock difference is 1 h 30 min in each direction.
$11:30 - 1 h 30 min = 10:00$ , so the answer is correct.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Converting 12-/24-hour time; elapsed time across midnight; timetables and journeys; time-zone differences; date changes; checking real-world scheduling answers.

Official curriculum source ↗

In this lesson

Understand the idea.

Use a common reference

Compare offsets first

See the method in action.

A half-hour difference

Compare destination and origin offsets.

Add the difference to the origin reading.

Check by converting back.

Across UTC

Find the signed offset change.

Move the clock seven hours ahead.

Check the shared UTC instant.

Try it yourself.

Check your understanding

Keep practising