Mathematics Standard • Year 11 • Module 2 • Lesson 20

Timetables and Elapsed Time — Skill Drill

Drill 12 ↔ 24-hour conversions and the count-up method for elapsed time, including journeys that cross midnight.

Build · Skill Drill

1. Quick recall

Answer each question in the space provided. 1 mark each

Q1.1 In 24-hour time:

Midnight = ____________ (start of day). Noon = ____________. 12:30 am = ____________. 12:30 pm = ____________.

Q1.2 If a journey starts at 22:15 and ends at 01:50 the next day, what number do we add to the finish time before subtracting the start time? ____________

Q1.3 Convert 2 h 35 min into total minutes: ____________ min, and into decimal hours (to 3 d.p.): ____________ h.

Stuck? Revisit lesson § Formula Panel — Time Conversions.

2. Worked example — elapsed time crossing midnight

Every line of working has a reason on the right.

Problem. An overnight bus departs at 11:32 pm and arrives at 5:18 am the next morning. Find the journey time.

Step 1 — Convert both times to 24-hour.

Depart 2332; arrive 0518.

Reason: pm adds 12 to the hour; am stays the same. 11 + 12 = 23.

Step 2 — Detect the midnight crossing.

0518 < 2332, so add 24 h to finish: 0518 + 2400 = 2918.

Reason: the finish is on the next day; treating it as "hours past the previous midnight" lets us subtract directly.

Step 3 — Count up via midnight.

2332 → 0000 = 28 min; 0000 → 0518 = 5 h 18 min.

Reason: count to midnight first, then add the time past midnight.

Conclusion. Total journey = 28 min + 5 h 18 min = 5 h 46 min.

3. Faded example — fill in the missing steps

A shift starts at 10:15 pm and ends at 6:40 am the next morning. Find the shift length using the count-up method. 4 marks

Step 1 — Convert to 24-hour: depart ____________, arrive ____________.

Step 2 — Detect midnight crossing: finish ____ start, so the journey crosses midnight.

Step 3 — Count up to midnight: from ____________ to 0000 = ____ h ____ min.

Step 4 — Count past midnight: 0000 to ____________ = ____ h ____ min.

Conclusion. Total shift = ____ h ____ min.

Stuck? Revisit lesson § Worked Example 2 — Crossing Midnight.

4. Graduated practice — conversions and elapsed time

Show your working. Write all final times in 24-hour or h–min format as requested.

Foundation — single-step conversions (4 questions)

Q	Problem	Answer
4.1 1	Convert 9:45 am to 24-hour time.
4.2 1	Convert 7:18 pm to 24-hour time.
4.3 1	Convert 1720 to 12-hour time.
4.4 1	Convert 0040 to 12-hour time.

Standard — typical HSC difficulty (6 questions)

Show at least one line of count-up working.

4.5 Find the elapsed time from 0815 to 1142. 2 marks

4.6 Find the elapsed time from 3:25 pm to 8:18 pm. 2 marks

4.7 Find the elapsed time from 11:48 pm to 2:33 am. 2 marks

4.8 A train departs at 1437. The journey takes 2 h 48 min. What is the arrival time (24-hour)? 2 marks

4.9 A movie starts at 7:42 pm and goes for 2 h 18 min. What time does it finish (12-hour)? 2 marks

4.10 An overnight nurse starts at 2245 and works for 8 h 30 min. What time (24-hour) does her shift end? 2 marks

Extension — timetable extracts (2 questions)

Use the bus timetable below for Q4.11 and Q4.12.

Stop Bus 1 Bus 2 Bus 3

Town Hall 0712 0743 0820

Library 0726 0757 0834

Hospital 0745 0816 0853

Airport 0808 0839 0916

4.11 A passenger boards Bus 2 at Library. How long does it take to reach the Airport? 3 marks

4.12 A passenger arrives at Hospital at 8:30 am. (a) Which bus can they catch? (b) What time does it reach the Airport? (c) How long do they wait at Hospital? 3 marks

Stuck? Find the row for Hospital and look for the next time AFTER 0830.

5. Self-check the easy 3

Tick once you've verified each.

For 4.2 (7:18 pm) I ADDED 12 to the hour (7 + 12 = 19) to get 1918, not 0718.

For 4.4 (0040) I converted to 12:40 am (just after midnight), not 12:40 pm.

For 4.7 I used the count-up method via midnight (not subtraction across midnight, which goes negative).

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers — Do not peek before attempting

Q1.1 — Reference times in 24-hour

Midnight = 0000. Noon = 1200. 12:30 am = 0030. 12:30 pm = 1230.

Q1.2 — Midnight-crossing adjustment

Add 2400 (24 hours) to the finish time before subtracting.

Q1.3 — 2 h 35 min

In minutes: 2 × 60 + 35 = 155 min. In decimal hours: 2 + 35/60 ≈ 2.583 h.

Q3 — Faded example (10:15 pm to 6:40 am)

Step 1: depart 2215, arrive 0640. Step 2: finish < start → crosses midnight. Step 3: 2215 to 0000 = 1 h 45 min. Step 4: 0000 to 0640 = 6 h 40 min. Conclusion: total = 8 h 25 min.

Q4.1 — 9:45 am → 24-hour

0945.

Q4.2 — 7:18 pm → 24-hour

7 + 12 = 19 → 1918.

Q4.3 — 1720 → 12-hour

17 − 12 = 5 → 5:20 pm.

Q4.4 — 0040 → 12-hour

Just after midnight → 12:40 am.

Q4.5 — 0815 to 1142

Hours: 11 − 8 = 3 h; minutes: 42 − 15 = 27 min. Total = 3 h 27 min.

Q4.6 — 3:25 pm to 8:18 pm

1525 to 2018; minutes: 18 − 25 → borrow: 78 − 25 = 53; hours: 19 − 15 = 4. Total = 4 h 53 min.

Q4.7 — 11:48 pm to 2:33 am

2348 to 0000 = 12 min; 0000 to 0233 = 2 h 33 min. Total = 2 h 45 min.

Q4.8 — 1437 + 2 h 48 min

Add hours: 1437 + 2 h = 1637; add 48 min: 37 + 48 = 85 = 1 h 25 → arrival = 1725.

Q4.9 — 7:42 pm + 2 h 18 min

7:42 pm = 1942. 1942 + 2 h = 2142; + 18 min: 42 + 18 = 60 = 1 h → 2200 + 0 min = 2200 (10:00 pm).

Q4.10 — 2245 + 8 h 30 min

2245 + 8 h = 3045 → subtract 2400 (rolls over midnight) = 0645; + 30 min = 0715.

Q4.11 — Bus 2 Library → Airport

Library 0757 → Airport 0839; minutes: 39 − 57 → borrow 1 h: 99 − 57 = 42; hours: 8 − 1 − 7 = 0 h → total = 42 min.

Q4.12 — Hospital at 0830

(a) Hospital times are 0745 (gone), 0816 (gone), 0853 (next). So Bus 3.
(b) Bus 3 reaches Airport at 0916 (9:16 am).
(c) Wait = 0853 − 0830 = 23 min.