Elapsed time across midnight | Year 8

01 / LEARN

Understand the idea.

Split at midnight

A clock repeats after midnight, but elapsed time keeps increasing. When the finish is on the next day, split the interval at midnight. Count to 00:00, count from there to the finish, then add those positive durations.

For 22:48 to 01:17 next day, there are 72 minutes before midnight and 77 afterwards. The clock reading 01:17 looks smaller than 22:48 because a new day has begun; it does not imply a negative duration.

Add minutes carefully

Hours and minutes regroup in sixties: $60 min = 1 h$ . When adding a duration, carry a full hour whenever the minutes reach 60. Each full 24 hours advances the date by one day.

Keep the day alongside any clock reading that crosses midnight. Check a duration by adding it back to the start. Decimal hours need a separate conversion: $1.5 h = 1 h 30 min$ because half an hour contains 30 minutes.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A late journey

Find the time from 22:48 until 01:17 the next day.

Worked solution

1
Count from the start to midnight.
$22:48 to 00:00 = 1 h 12 min$
There are 12 minutes to 23:00 and one further hour to midnight.
2
Count from midnight to the finish.
$00:00 to 01:17 = 1 h 17 min$
Both readings now belong to the following day.
3
Add the two intervals.
$1 h 12 min + 1 h 17 min = 2 h 29 min$
The two consecutive intervals cover the whole journey.

Answer

2 hours 29 minutes.

EXAMPLE 02

Finish after midnight

A job begins at 23:25 and lasts 2 h 50 min. When does it finish?

Worked solution

1
Find the time remaining before midnight.
$23:25 to 00:00 = 35 min$
Splitting at midnight makes the date change explicit.
2
Subtract that part from the duration.
$\begin{aligned} 2 h 50 min & = 170 min \\ 170 - 35 & = 135 min \end{aligned}$
The first 35 minutes have already been used before midnight.
3
Convert the remaining time and state the day.
$135 min = 2 h 15 min \Rightarrow 02:15 next day$
The remaining duration begins at midnight on the next day.

Answer

02:15 the next day.

03 / YOUR TURN

Try it yourself.

Check your understanding

How long is 23:40 to 00:25 the next day?

Show answer & reasoning

45 minutes.

There are 20 minutes from 23:40 to midnight and another 25 minutes to 00:25. Thus $20 + 25 = 45$ minutes.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Find the time from 23:15 to 00:05 the next day.
2 marks
Find the time from 21:40 to 02:10 the next day.
2 marks
Add 1 h 35 min to 23:10.
2 marks
A shift runs from 18:30 to 01:00 the next day. Find its duration.
2 marks
An event finishes at 00:20 Tuesday after lasting 2 h 45 min. When did it start?
2 marks
Convert 2.5 hours to hours and minutes, then add it to 22:50.
2 marks

Read the worked solutions

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

Find the time from 23:15 to 00:05 the next day.
2 marks
$45 min to midnight + 5 min = 50 min$ .
50 minutes.
Find the time from 21:40 to 02:10 the next day.
2 marks
$2 h 20 min + 2 h 10 min = 4 h 30 min$ .
4 h 30 min.
Add 1 h 35 min to 23:10.
2 marks
50 min reach midnight; another 45 min remain.
00:45 next day.
A shift runs from 18:30 to 01:00 the next day. Find its duration.
2 marks
$5 h 30 min until midnight + 1 h = 6 h 30 min$ .
6 h 30 min.
An event finishes at 00:20 Tuesday after lasting 2 h 45 min. When did it start?
2 marks
Subtract 20 min to 00:00 Tuesday; another 2 h 25 min takes you back to 21:35 Monday.
21:35 Monday.
Convert 2.5 hours to hours and minutes, then add it to 22:50.
2 marks
$0.5 \times 60 = 30$ min.
$22:50 + 2 h 30 min = 01:20$ next day.
2 h 30 min; finish 01:20 next day.

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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.

Split at midnight

Add minutes carefully

See the method in action.

A late journey

Count from the start to midnight.

Count from midnight to the finish.

Add the two intervals.

Finish after midnight

Find the time remaining before midnight.

Subtract that part from the duration.

Convert the remaining time and state the day.

Try it yourself.

Check your understanding

Keep practising