Year 8 Maths Time and Travel

Time Differences

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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