Reading a timetable and calculating how long a journey takes sounds simple — until the train crosses midnight or the flight has a 2-hour layover. Master the structured method and nothing trips you up.
45–50 minMS-M33 MC3 SALesson 20 of 22Free
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A train departs Sydney at 11:48 pm and arrives in Newcastle at 1:23 am the next day. Your friend says the journey is "1 hour and 35 minutes." How would you check this? Is there a reliable method that doesn't rely on mental arithmetic — one that works even when the clock crosses midnight?
Type your initial response below — you will revisit this at the end of the lesson.
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Write your initial thinking in your book
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Come back to this at the end of the lesson.
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Time Conversions — This Lesson
$1 \text{ h} = 60 \text{ min} = 3600 \text{ s}$
To convert minutes to hours: divide by 60To convert hours to minutes: multiply by 60e.g. 2 h 35 min $= 2 + \frac{35}{60} = 2.58\overline{3}$ h (decimal) or write as 155 min
24-hour ↔ 12-hour conversion
12-hour am: same as 24-hour (e.g. 9:45 am = 0945)12-hour pm: add 12 hours (e.g. 3:20 pm = 1520)Midnight = 0000 (start of day) or 2400 (end of day)Noon = 1200
Elapsed time = finish time $-$ start time
Convert both times to 24-hour before subtractingIf result crosses midnight, add 24 hours to the finish timeMethod: count hours, then count remaining minutes
🧠 Know
How to convert between 12-hour and 24-hour time
Midnight = 0000 (or 2400), Noon = 1200
How to calculate elapsed time by subtracting start from finish
How to handle elapsed time that crosses midnight
💡 Understand
Why 24-hour time eliminates the am/pm ambiguity
Why you can't just subtract when the finish time crosses midnight (add 24 h first)
How timetable columns relate to different services/vehicles
✅ Can Do
Read train, bus, or flight timetables and extract relevant information
Calculate journey times including layovers and connections
Calculate elapsed time across midnight
Convert between hours:minutes and decimal hours
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Key Terms
24-hour timeA time format using four digits (HHMM) from 0000 to 2359, eliminating am/pm ambiguity; e.g. 1435 = 2:35 pm
Elapsed timeThe total time between a start and finish event; calculated as finish time minus start time (in the same format)
TimetableA table listing scheduled departure and arrival times for transport services; each column typically represents one service
Layover / connection timeThe waiting time between arriving on one service and departing on the next; must be added when calculating total travel time
Misconceptions to Fix
✗
Wrong: Rounding 4.5 down gives 4.
✗
Right: Standard rounding rounds 4.5 up to 5; rounding to the nearest even number (banker's rounding) is different.
12-Hour and 24-Hour Time
Key Point
Always check your units before substituting into formulas. Converting to consistent units is a common source of errors in assessment tasks.
Key Terms
FormulaA rule showing the relationship between variables using symbols.
SubstitutionReplacing variables with their known values in an equation.
Unit ConversionChanging a measurement from one unit to another.
CapacityThe amount of liquid a container can hold, measured in litres or millilitres.
PerimeterThe total distance around the outside of a shape.
AreaThe amount of space inside a two-dimensional shape.
Converting Between Time Formats
The 24-hour clock avoids all ambiguity: there is no need to specify am or pm. It is used universally in transport timetables, the military, and aviation.
12-hour time
24-hour time
Rule
12:00 midnight
0000
Start of day
12:30 am
0030
am: write directly (add leading zero if needed)
9:15 am
0915
am: same digits
12:00 noon
1200
Noon stays as 1200
1:00 pm
1300
pm: add 12 to the hour (1 + 12 = 13)
7:45 pm
1945
pm: 7 + 12 = 19 → 1945
11:59 pm
2359
pm: 11 + 12 = 23 → 2359
Common error — the 12 pm trap: Many students convert 12:30 pm to 0030 (treating noon like midnight). Remember: 12 pm (noon) = 1200 in 24-hour time. Only 12 am (midnight) = 0000. Everything else above noon gets +12.
Calculating Elapsed Time
The Count-Up Method
The most reliable method for elapsed time is to count up from the start time to the finish time in two stages: first count whole hours, then count remaining minutes.
Step 1: Write both times in 24-hour format
Step 2: Count hours from start to a "round" time near finish
Step 3: Count remaining minutes
Step 4: Add the hours and minutes together
Must do — crossing midnight: If the journey crosses midnight (finish time in 24-hour is less than start time), add 24:00 to the finish time before subtracting. e.g. depart 2348, arrive 0125: add 24 to finish → 25:25 − 23:48 = 1 h 37 min.
Worked Example 1Elapsed Time — No Midnight Crossing
Problem
A bus departs at 10:47 am and arrives at 2:23 pm. How long does the journey take?
3(b) 8:40 am = 0840; Service B departs Parramatta at 0843 ✓; arrives Penrith 0925Service A departs 0814 (already gone); Service B departs 0843 (next available); Service C departs 0929 (later)
4(c) Wait = $0843 - 0840 = \mathbf{3 \text{ min}}$Arrives 0840, next service departs 0843
Practice
Practice Questions
Section A — Time Conversion
Convert to 24-hour time: (a) 7:20 am (b) 4:55 pm (c) 12:10 am (d) 12:30 pm
A night bus departs at 10:40 pm and arrives at 2:05 am. Find the journey time.
A shift starts at 2330 and ends at 0645 the next morning. How long is the shift?
Section C — Timetable Problems
Use this bus timetable for Questions 7–9:
Town Hall
Bus 1:0722
Bus 2:0755
Bus 3:0835
Museum
Bus 1:0731
Bus 2:0804
Bus 3:0844
Waterloo
Bus 1:0748
Bus 2:0821
Bus 3:0901
Airport
Bus 1:0810
Bus 2:0843
Bus 3:0923
A passenger boards Bus 2 at Town Hall. How long does it take to reach the Airport?
A passenger arrives at Waterloo at 8:15 am. Which is the next bus, and when does it reach the Airport?
A passenger needs to be at the Airport no later than 8:50 am. Which is the latest bus they can take from Town Hall?
Q1
(a) 0720 (b) 1655 (c) 0010 (d) 1230
Q2
(a) 6:35 am (b) 2:10 pm (c) 12:05 am (d) 10:58 pm
Q3
$1327 - 0845$: mins $27-45$ → borrow: $87-45=42$ min; hrs $12-9=3$ h; total $= \mathbf{4\text{ h }42\text{ min}}$
Q4
1515 to 1952: $52-15=37$ min; $19-15=4$ h; $= \mathbf{4\text{ h }37\text{ min}}$
Q5
Depart 2240, arrive 0205; add 2400: $2605-2240$: $65-40=25$ min; $26-22=4$ h (but borrow applies)... counting: 2240→0000 = 80 min; 0000→0205 = 2h 5min; total = $\mathbf{3\text{ h }25\text{ min}}$
Q6
2330→0000 = 30 min; 0000→0645 = 6h 45min; total = $\mathbf{7\text{ h }15\text{ min}}$
Q7
$0843 - 0755 = \mathbf{48\text{ min}}$
Q8
8:15 am = 0815; Bus 2 at Waterloo departs 0821 (next available); arrives Airport $\mathbf{0843}$ (8:43 am)
Q9
Bus 2 arrives Airport at 0843 (before 0850 ✓); Bus 3 arrives 0923 (too late); latest bus from Town Hall is $\mathbf{\text{Bus 2}}$ at 0755
Revisit Your Initial Thinking
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
Multiple Choice
1 A train departs at 7:54 pm and arrives at 11:22 pm. The journey time is:
A 3 h 32 min
B 3 h 28 min
C 4 h 32 min
D 3 h 22 min
? Regarding this topic, 1 A train departs at 7:54 pm and arrives at 11:22 pm. The journey time is:
A 3 h 32 min
B 3 h 28 min
C 4 h 32 min
D 3 h 22 min
B - Correct!
B — 1954 to 2322: mins $22-54$ → borrow 1 h: $82-54=28$ min; hrs $23-20=3$ h (after borrow $22-19=3$). Total = 3 h 28 min.
2 In 24-hour time, 12:15 am is written as:
A 1215
B 0015
C 2415
D 0015 or 2415
? Regarding this topic, 2 In 24-hour time, 12:15 am is written as:
A 1215
B 0015
C 2415
D 0015 or 2415
B - Correct!
B — 12:15 am is 15 minutes after midnight, so 0015. Option A (1215) is 12:15 pm (noon). 2415 is not a valid 24-hr time.
3 A flight departs at 2245 and lands at 0630 the next day. The flight duration is:
A 7 h 55 min
B 8 h 45 min
C 16 h 15 min
D 7 h 45 min
? Regarding this topic, 3 A flight departs at 2245 and lands at 0630 the next day. The flight duration is:
A 7 h 55 min
B 8 h 45 min
C 16 h 15 min
D 7 h 45 min
A - Correct!
A — Count: 2245 to 0000 = 1 h 15 min; 0000 to 0630 = 6 h 30 min; total = 7 h 45 min. Wait — 1h15 + 6h30 = 7h45 min. Rechecking: 2245→2300 = 15 min; 2300→0000 = 60 min; 0000→0630 = 390 min; total = 15+60+390 = 465 min = 7 h 45 min → answer is D 7 h 45 min.
Short Answer
01
SA 43 marks
A student works a shift from 6:45 pm to 1:10 am.
(a) Write both times in 24-hour format. (1 mark)
(b) Calculate the length of the shift in hours and minutes. (2 marks)
Work in your book
Saved
(a)
6:45 pm = 1845; 1:10 am = 0110
(b)
Crosses midnight: 1845 to 0000 = 3 h 15 min; 0000 to 0110 = 1 h 10 min; total = 6 h 25 min
02
SA 54 marks
Use the timetable from Worked Example 3 (Service A, B, C between Central and Penrith).
(a) How long does Service B take from Central to Penrith? (1 mark)
(b) A passenger arrives at Strathfield at 8:30 am. What is the earliest service they can catch, and when does it reach Penrith? (2 marks)
(c) How much longer does Service C take from Central to Penrith compared to Service A? (1 mark)
Work in your book
Saved
(a)
$0925 - 0812 = 1\text{ h }13\text{ min}$ — same as Service A
(b)
8:30 am = 0830; Service B at Strathfield = 0827 (already gone); Service C at Strathfield = 0912 (next). Service C arrives Penrith at 1011 (10:11 am)
(c)
Service A: 1 h 13 min; Service C: $1011-0857 = 1\text{ h }14\text{ min}$; difference = 1 min
03
SA 64 marks
A flight from Sydney departs at 2150. It has a 1 hour 40 minute layover in Singapore. The second leg takes 6 hours 15 minutes and lands in London.
(a) The first leg (Sydney to Singapore) takes 8 hours 20 minutes. At what 24-hour time does the plane land in Singapore? (2 marks)
(b) At what 24-hour time does the plane depart Singapore? (1 mark)
(c) What is the total elapsed time from Sydney departure to London arrival? (1 mark)