Year 8 Maths Time and Travel

Time Differences

20 practice questions 1 video lesson Theory + worked examples

Time differences are about how long something takes, from a cafe shift to a cricket Test lasting several days. In NSW Year 8 maths this consolidates time calculations from earlier years in 24-hour time, and links to time zones, which are worked with integers (NESA outcome MA4‑INT‑C‑01).

You will count on and back in easy jumps, cross midnight, add and subtract hours and minutes, and find durations over several days, such as a Sydney to Hobart yacht race. You will turn shifts with unpaid breaks into pay, and find flight and coach times when the departure and arrival are in different time zones. Rosters, timetables and travel plans all depend on these skills. It is part of Year 8 Time and Travel.

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Practice questions

Every question with a fully worked solution.

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Time Differences - Video - How To Add and Subtract Time in Hours and Minutes Watch

Theory

A time difference is the time from one moment to another. Count on from the earlier time in easy jumps and add them: from 16:45 to 21:20 is $15$ min $+$ $4$ h $+$ $20$ min $=$ $4$ h $35$ min. This Year 8 maths page shows how, including midnight and pay.

24-hour time runs from 00:00 (midnight) to 23:59; 14:35 is 2:35 pm. Answer a 24-hour question in 24-hour time.

Between two times: jump to the next o’clock, then whole hours, then the minutes left. Add the jumps.

Past midnight: stop at 00:00, then keep counting into the new day, and say which day the answer is on.

Working backwards: count back to the o’clock, then to 00:00, then into the day before. Check by counting on again.

Adding durations: add the hours, add the minutes, then regroup: $5$ h $90$ min $= 6$ h $30$ min. For several days, count whole days first ($1$ day $= 24$ h).

Hours worked and pay: take off any unpaid break, change to decimal hours by dividing the minutes by $60$ ($8$ h $15$ min $= 8.25$ h), then pay $=$ hours $\times$ hourly rate.

Across a time zone: put both times on one clock first, then count on.

Australia’s clocks. WA uses AWST (UTC$+8$); the NT and SA use ACST (UTC$+9{:}30$); QLD, NSW, the ACT, VIC and TAS use AEST (UTC$+10$). From the first Sunday in October to the first Sunday in April, SA uses ACDT (UTC$+10{:}30$) and NSW, the ACT, VIC and TAS use AEDT (UTC$+11$); WA, the NT and QLD do not change.

Counting on from 22:35 to 01:50 the next morning, with a stop at midnight: $25$ min $+$ $1$ h $+$ $1$ h $50$ min $=$ $3$ h $15$ min.

Australian time zones (daylight saving runs from the first Sunday in October to the first Sunday in April):

State or territory	Standard time	Daylight saving time
WA	AWST, UTC$+8$	none (stays UTC$+8$)
NT	ACST, UTC$+9{:}30$	none (stays UTC$+9{:}30$)
SA	ACST, UTC$+9{:}30$	ACDT, UTC$+10{:}30$
QLD	AEST, UTC$+10$	none (stays UTC$+10$)
NSW, ACT, VIC, TAS	AEST, UTC$+10$	AEDT, UTC$+11$

Minutes as decimal hours (for pay):

Minutes	15	20	30	40	45
Hours	0.25	$0.\dot{3}$	0.5	$0.\dot{6}$	0.75

          Finish the regrouping. \(3\) h \(75\) min is not an answer: it is \(4\) h \(15\) min.
        

          Do not subtract clock numbers across midnight. From 22:50 to 05:05 is \(6\) h \(15\) min, found by jumping to 00:00 first.
        

Finding a time difference

Jump from the start to the next o’clock.
Jump whole hours (stopping at midnight if needed).
Jump the minutes left.
Add the jumps and regroup $60$ min as $1$ h.

Example 1 — Counting on

Calculate the time difference between 16:45 and 21:20.

Solution

16:45 $\to$ 17:00 is $15$ min; 17:00 $\to$ 21:00 is $4$ h; 21:00 $\to$ 21:20 is $20$ min.

$4$ h $35$ min

Example 2 — Adding a duration

What time is it $3$ h $10$ min after 7:25 am?

Solution

7:25 am $+$ $3$ h $=$ 10:25 am; then $+$ $10$ min.

10:35 am

Example 3 — Across midnight

A freight train leaves at 21:35 and arrives at 06:08 the next morning. How long is the trip?

Solution

21:35 $\to$ 22:00: $25$ min. 22:00 $\to$ 00:00: $2$ h. 00:00 $\to$ 06:00: $6$ h. 06:00 $\to$ 06:08: $8$ min.

$8$ h $33$ min

Example 4 — Working backwards

A plane lands at 01:05 on Saturday after $7$ h $25$ min in the air. When did it take off?

Solution

01:05 $-$ $1$ h $5$ min $=$ 00:00 Sat; $-$ $6$ h $=$ 18:00 Fri; $-$ $20$ min $=$ 17:40 Fri.

$65 + 360 + 20$

$=$

$445$

1740 Friday

17:40 on Friday. Check: $445$ min $= 7$ h $25$ min.

Example 5 — Hours worked and pay

Sam works from 12:50 to 19:05 with a $30$-minute unpaid break. She is paid $\$21.20$ an hour. How much does she earn?

Solution

12:50 $\to$ 19:05 is $6$ h $15$ min; minus the break is $5$ h $45$ min $= 5.75$ h.

$5.75 \times 21.20$

$=$

$121.90$

$ 121.90

$\$121.90$

Example 6 — One clock first

In June, a plane leaves a city on AEST (UTC$+10$) at 22:15 on Friday and lands in a city on AWST (UTC$+8$) at 01:50 on Saturday, local time. How long is the flight?

Solution

AEST is $2$ h ahead, so the landing is 03:50 Saturday on the AEST clock. Count on: 22:15 $\to$ 00:00 is $1$ h $45$ min; 00:00 $\to$ 03:50 is $3$ h $50$ min.

$4$ h $95$ min $= 5$ h $35$ min

Example 7 — Durations, days and intervals

(i) Add $3$ h $48$ min and $2$ h $35$ min.
(ii) How long is it from 09:15 on Wednesday to 14:50 on Friday?
(iii) Buses leave every $1$ h $35$ min from 06:50. List the first four times.

Solution

(i) $5$ h $83$ min; regroup $60$ min.
(ii) Wednesday 09:15 to Friday 09:15 is $2$ days $= 48$ h; then $5$ h $35$ min more.

(i) $6$ h $23$ min
(ii) $53$ h $35$ min ($2$ days $5$ h $35$ min)
(iii) 06:50, 08:25, 10:00, 11:35

Common pitfalls

Leaving 60 or more minutes. Regroup every 60 minutes as 1 hour.

Subtracting across midnight. Count on to 00:00 first, then into the next day.

Writing 7 h 30 min as 7.3 h. Divide the minutes by $60$: $7.5$ h.

Comparing times on two different clocks. Change one time onto the other clock first.

Frequently asked questions

How do I find the time between two times?

Count on from the earlier time: to the next o’clock, then whole hours, then the minutes left, and add the jumps.

How do I find a time difference across midnight?

Count on to 00:00, then continue into the next day.

How do I change hours and minutes to decimal hours?

Divide the minutes by 60. For example, 5 h 45 min is 5.75 h.

How do I add 2 h 50 min to 3 h 25 min?

Add hours and minutes separately to get 5 h 75 min, then regroup to 6 h 15 min.

What is 14:35 in 12-hour time?

2:35 pm.

State or territory	Standard time	Daylight saving time
WA	AWST, UTC\(+8\)	none (stays UTC\(+8\))
NT	ACST, UTC\(+9{:}30\)	none (stays UTC\(+9{:}30\))
SA	ACST, UTC\(+9{:}30\)	ACDT, UTC\(+10{:}30\)
QLD	AEST, UTC\(+10\)	none (stays UTC\(+10\))
NSW, ACT, VIC, TAS	AEST, UTC\(+10\)	AEDT, UTC\(+11\)

Time Differences

📖 Theory

Finding a time difference

Common pitfalls

Frequently asked questions

Theory