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hscscience Maths Std · Y11
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Module 2 · MS-M3 · L20 of 22 ~50 min ⚡ +95 XP available

Timetables and Elapsed Time

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.

Today's hook, 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." Is that right? And how do you reliably check it, even when the clock crosses midnight?
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The key facts you need to own

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Worksheets

Practise this lesson

Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

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01
Think First, your gut answer first
+5 XP warm-up

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."

Without calculating 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?

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Come back to this at the end of the lesson.

02
The key facts you need to own
+5 XP to read

Time calculations hinge on two skills: converting between 12-hr and 24-hr time, and calculating elapsed time reliably, even across midnight.

24-hour time uses four digits (HHMM) from 0000 to 2359. There is no am/pm, midnight = 0000, noon = 1200.

To convert pm to 24-hr: add 12 to the hour. (Exception: 12 pm stays as 1200; 12 am = 0000.)

Converting between 12-hour and 24-hour clock times.
Elapsed time $=$ finish $-$ start (add 24 h if crossing midnight)
Comparison table mapping 12-hour times to 24-hour times Elapsed time count-up method, two worked examples as parallel lists
am times
Write the same digits with a leading zero. e.g. 9:15 am = 0915. Midnight (12:00 am) = 0000.
pm times
Add 12 to the hour. e.g. 7:45 pm = 1945. Noon (12:00 pm) = 1200 (already correct).
Crossing midnight
Add 2400 to the finish time before subtracting. e.g. depart 2348, arrive 0125: $2525 - 2348 = 1$ h 37 min.
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What you'll master
Know

Key facts

  • How to convert between 12-hour and 24-hour time
  • 60 seconds = 1 minute, 60 minutes = 1 hour, 3600 seconds = 1 hour
  • 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

Concepts

  • 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

Skills

  • Read train, bus, or flight timetables and extract relevant information
  • Calculate journey times including layovers and connections
  • Calculate elapsed time across midnight
  • Convert between seconds, minutes and hours, writing any remainder as the next unit down
  • Convert between hours:minutes and decimal hours
04
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.
Decimal hoursA length of time written as one number of hours, with the minutes turned into a fraction of an hour instead of being counted separately. Like this: a 3 hour 45 minute shift is 3.75 hours, because 45 ÷ 60 = 0.75. Timesheets use it so that pay is just hours × rate.
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Converting between time formats

The 24-hour clock avoids all ambiguity: there is no need to specify am or pm.

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Converting between time formats
core concept

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 time24-hour timeRule
12:00 midnight0000Start of day
12:30 am0030am: write directly (add leading zero if needed)
9:15 am0915am: same digits
12:00 noon1200Noon stays as 1200
1:00 pm1300pm: add 12 to the hour (1 + 12 = 13)
7:45 pm1945pm: 7 + 12 = 19 → 1945
11:59 pm2359pm: 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.

24-hour clock: no am/pm. 0000 = midnight; 1200 = noon; 1800 = 6 pm. Converting 12-hour pm to 24-hour: add 12 (except 12 pm = 1200). Converting 24-hour ≥ 1300 to 12-hour: subtract 12 and add pm. Midnight = 0000 or 2400.

Pause, copy the 24-hour clock conversion rules: 12-hour pm → 24-hour: add 12 (except 12:00 pm = 1200); 24-hour ≥ 1300 → 12-hour: subtract 12 and add "pm"; midnight = 0000 (start of day) or 2400 (end of day), and note that 1200 is noon, not midnight into your book.

Did you get this? True or false: 12:30 pm in 24-hour time is written as 0030.

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Seconds, minutes and hours

Time is the one measurement that does not run in tens.

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Seconds, minutes and hours
core concept

Time is the one measurement that does not run in tens. There are 60 seconds in a minute and 60 minutes in an hour, so every step up or down the ladder is a 60, never a 10. Going down the ladder (bigger unit to smaller unit) you multiply. Going up the ladder you divide.

ConversionDo thisExample
hours → minutes× 603 h = 3 × 60 = 180 min
minutes → seconds× 607 min = 7 × 60 = 420 s
hours → seconds× 60 × 60 (that is × 3600)2 h = 2 × 3600 = 7200 s
seconds → minutes÷ 60540 s = 540 ÷ 60 = 9 min
minutes → hours÷ 60150 min = 150 ÷ 60 = 2.5 h
seconds → hours÷ 360010 800 s = 10 800 ÷ 3600 = 3 h

Leftovers become the next unit down. When a division does not come out whole, the remainder is not a decimal, it is the smaller unit. To write 200 seconds in minutes and seconds: 200 ÷ 60 = 3 remainder 20, so 200 s = 3 min 20 s. Same idea for minutes into hours: 145 min = 2 h 25 min, because 145 ÷ 60 = 2 remainder 25.

Decimal hours are different again. Pay sheets, speed calculations and timesheets often want hours as a single decimal number rather than hours and minutes. To turn the minutes part into a decimal, divide it by 60. To go back, multiply the decimal part by 60.

3 h 45 min → decimal: 45 ÷ 60 = 0.75, so 3 h 45 min = 3.75 h

2.4 h → hours and minutes: 0.4 × 60 = 24, so 2.4 h = 2 h 24 min

Common error, reading the decimal as minutes: 2.5 hours is not 2 hours 5 minutes, and 3.15 hours is not 3 hours 15 minutes. The digits after the point are a fraction of an hour, not a count of minutes. 2.5 h = 2 h 30 min, and 3.15 h = 3 h 9 min, because 0.15 × 60 = 9.

60 s = 1 min, 60 min = 1 h, 3600 s = 1 h. Bigger unit to smaller: multiply by 60. Smaller unit to bigger: divide by 60. A remainder is the next unit down, so 200 s = 3 min 20 s. Minutes to decimal hours: divide by 60 (45 min = 0.75 h). Decimal hours to minutes: multiply the decimal part by 60 (2.4 h = 2 h 24 min).

Pause, copy the time-unit ladder into your book: 60 s = 1 min, 60 min = 1 h, 3600 s = 1 h; multiply by 60 going down, divide by 60 going up, and write any remainder as the next unit down. Add the two decimal-hour rules underneath: minutes to decimal is divide by 60, decimal to minutes is multiply by 60, and 2.5 h means 2 h 30 min.

Fill the gap: A ferry crossing takes 195 minutes. In hours and minutes that is , because 195 ÷ 60 = 3 remainder . Written as a decimal number of hours it is h. A 4 minute delay is seconds.

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Worked examples · 3 in a row, reveal as you go

Worked examples · 3 in a row, reveal as you go

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · ELAPSED TIME, NO MIDNIGHT CROSSING

A bus departs at 10:47 am and arrives at 2:23 pm. How long does the journey take?

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Convert: depart $1047$, arrive $1423$
10:47 am = 1047; 2:23 pm → 2 + 12 = 14 → 1423.
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PROBLEM 2 · ELAPSED TIME, CROSSING MIDNIGHT

An overnight train departs at 11:48 pm and arrives at 6:15 am the next morning. Find the journey time.

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Convert: depart $2348$, arrive $0615$
11:48 pm → 11 + 12 = 23 → 2348; 6:15 am = 0615.
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PROBLEM 3 · READING A TIMETABLE

Use the train timetable extract below.
(a) How long does Service A take from Central to Penrith?
(b) A passenger arrives at Parramatta at 8:40 am. Which is the next service they can catch, and when does it arrive in Penrith?
(c) How long must the passenger wait at Parramatta?

StationService AService BService C
Central074308120857
Strathfield075808270912
Parramatta081408430929
Blacktown082908580944
Penrith085609251011
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(a) Service A: depart Central $0743$, arrive Penrith $0856$
Read directly from timetable column A.
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Quick check: A shift starts at 2230 and ends at 0115 the next day. What is the correct method for finding the elapsed time?

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Common errors · the 3 traps that cost marks

Common errors · the 3 traps that cost marks

Common errors · the 3 traps that cost marks

Trap 01
The 12 pm / 12 am trap
12 pm (noon) = 1200, not 0000. 12 am (midnight) = 0000, not 1200. These two are swapped by many students every year, write this rule at the top of your working.
Trap 02
Subtracting minutes that are too small
If the minutes digit of the finish time is smaller than the start (e.g. 1423 − 1047), you must borrow 1 hour (60 min) from the hours column. e.g. $83 - 47 = 36$ min, then $13 - 10 - 1 = 2$ h → wait: always use count-up to avoid this entirely.
Trap 03
Forgetting to add 2400 when crossing midnight
If the finish time is less than the start time (e.g. finish 0115, start 2230), you must add 2400 to the finish before subtracting. Forgetting this gives a negative, or wrong, answer every time.

Fill the gap: A night bus departs at 10:40 pm and arrives at 2:05 am. In 24-hour time, departure = and arrival = . Since arrival < departure, add 2400: adjusted arrival = . Elapsed time = 2605 − 2240 = .

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Revisit your thinking

Quick-fire practice · 7 questions

Quick-fire practice · 7 questions

1

Convert to 24-hour time: (a) 7:20 am   (b) 4:55 pm   (c) 12:10 am   (d) 12:30 pm

2

Convert to 12-hour time: (a) 0635   (b) 1410   (c) 0005   (d) 2258

3

Find the elapsed time from 0845 to 1327.

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A night bus departs at 10:40 pm and arrives at 2:05 am. Find the journey time.

5

A shift starts at 2330 and ends at 0645 the next morning. How long is the shift?

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Convert: (a) 4 min to seconds   (b) 2 h to seconds   (c) 330 s to minutes   (d) 260 min to hours and minutes

7

Write as decimal hours: (a) 1 h 30 min   (b) 6 h 12 min. Then write as hours and minutes: (c) 4.75 h   (d) 2.1 h

Two truths, one lie: Three statements below are correct. Which one is the lie?

Odd one out: Three of these are valid elapsed-time scenarios. Which one requires a different technique?

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Revisit your thinking

Look back at what you wrote in the Think First section. Let's check: depart 11:48 pm = 2348; arrive 1:23 am = 0125. Count: 2348 → 0000 = 12 min; 0000 → 0125 = 1 h 25 min. Total = 1 h 37 min. Your friend said 1 h 35 min, only 2 minutes out, but the method matters for larger journeys.

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Show what you have learned

Multiple choice, then short answer under exam conditions.

01
Multiple choice
+5 XP per correct · +25 XP all-correct

Pick your answer, then rate your confidence. That tells the system what to drill next. Each retry pulls a fresh mix from the bank.

02
Short answer
ApplyBand 43 marks

Q1. 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)

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ApplyBand 44 marks

Q2. 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)

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AnalyseBand 54 marks

Q3. 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)

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ApplyBand 44 marks

Q4. A casual worker is paid $\$28.40$ per hour and records each shift to the nearest minute.
(a) Monday's shift ran 5 h 24 min. Write this as a decimal number of hours.  (1 mark)
(b) Tuesday's shift is recorded as 6.75 h. Write this in hours and minutes.  (1 mark)
(c) A machine cycle takes 150 seconds. How many whole cycles run in one hour?  (1 mark)
(d) Calculate the worker's pay for Monday.  (1 mark)

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📖 Comprehensive answers (click to reveal)

Drill 1: (a) 0720   (b) 1655   (c) 0010   (d) 1230

Drill 2: (a) 6:35 am   (b) 2:10 pm   (c) 12:05 am   (d) 10:58 pm

Drill 3: $1327 - 0845$: count-up: 0845 + 4 h = 1245; 1245 → 1327 = 42 min; total = $\mathbf{4\text{ h }42\text{ min}}$

Drill 4: Depart 2240, arrive 0205; add 2400: $2605 - 2240$: 40 min to midnight (2240→2300=20, 2300→0000=60, 0000→0205=2h5); count: 2240→0000 = 80 min; 0000→0205 = 2h5; total = $\mathbf{3\text{ h }25\text{ min}}$

Drill 5: 2330→0000 = 30 min; 0000→0645 = 6h 45min; total = $\mathbf{7\text{ h }15\text{ min}}$

Drill 6: (a) $4 \times 60 = \mathbf{240\text{ s}}$   (b) $2 \times 3600 = \mathbf{7200\text{ s}}$   (c) $330 \div 60 = \mathbf{5.5\text{ min}}$ (or 5 min 30 s)   (d) $260 \div 60 = 4$ remainder $20$, so $\mathbf{4\text{ h }20\text{ min}}$

Drill 7: (a) $30 \div 60 = 0.5$, so $\mathbf{1.5\text{ h}}$   (b) $12 \div 60 = 0.2$, so $\mathbf{6.2\text{ h}}$   (c) $0.75 \times 60 = 45$, so $\mathbf{4\text{ h }45\text{ min}}$   (d) $0.1 \times 60 = 6$, so $\mathbf{2\text{ h }6\text{ min}}$ (not 2 h 10 min)

Q1 (3 marks): (a) 6:45 pm = 1845; 1:10 am = 0110 [1]. (b) 1845 to 0000 = 3 h 15 min; 0000 to 0110 = 1 h 10 min; total = 6 h 25 min [2].

Q2 (4 marks): (a) $0925 - 0812 = \mathbf{1\text{ h }13\text{ min}}$ [1]. (b) 8:30 am = 0830; Service B at Strathfield = 0827 (already gone); Service C at Strathfield = 0912 (next). Service C arrives Penrith at 1011 [2]. (c) Service A: 1 h 13 min; Service C: $1011-0857 = 1\text{ h }14\text{ min}$; difference = 1 min [1].

Q3 (4 marks): (a) $2150 + 8\text{h}\,20 = 2150 + 8\text{h} = 0550 + 20\text{min} = \mathbf{0610}$ (next day) [2]. (b) $0610 + 1\text{h}\,40 = \mathbf{0750}$ [1]. (c) Total = 8h20 + 1h40 + 6h15 = 16 h 15 min [1].

Q4 (4 marks): (a) $24 \div 60 = 0.4$, so 5 h 24 min = 5.4 h [1]. (b) $0.75 \times 60 = 45$, so 6.75 h = 6 h 45 min [1]. (c) 1 h = 3600 s; $3600 \div 150 = 24$, so 24 whole cycles [1]. (d) $5.4 \times \$28.40 = \mathbf{\$153.36}$ [1]. Note (d) is why (a) matters: pay is decimal hours × rate, so reading "5 h 24 min" as $5.24$ hours would give $\$148.82$, underpaying by $\$4.54$ on a single shift.