Mathematics Standard • Year 11 • Module 2 • Lesson 20
Timetables and Elapsed Time, Problem Set
Apply 24-hour time, elapsed time and timetable reading to real Sydney transport scenarios, including shifts, connections and international flights.
Problem 1, Sydney Trains Western Line timetable
Use this train timetable extract.
Station Service A Service B Service C
Central 0717 0748 0832
Strathfield 0732 0803 0847
Parramatta 0748 0819 0904
Blacktown 0803 0834 0919
Penrith 0830 0901 0946
Set up: What are we solving for?
(i) How long does Service A take from Central to Penrith? 1 mark
(ii) A passenger arrives at Parramatta at 0825. Which is the next service they can catch, and at what time does it reach Penrith? 2 marks
(iii) How much longer does Service C take from Central to Penrith compared to Service A? 2 marks
Stuck? Find each Central → Penrith elapsed time first, then subtract.Problem 2, Hospital nurse night shift
A nurse signs on at 7:45 pm on a Tuesday and signs off at 7:18 am on Wednesday.
Set up: What are we solving for?
(i) Write both times in 24-hour format. 1 mark
(ii) Calculate the total shift length in hours and minutes. 2 marks
(iii) Convert the shift length to decimal hours, to 2 d.p., and calculate her pay if she earns $42.60 per hour. 2 marks
Stuck? Count up via midnight; then convert h–min to decimal hours by dividing minutes by 60.Problem 3, Connecting buses with a layover
A student boards Bus 1 at City stop at 0832. Bus 1 takes 47 minutes to reach Hub stop. At Hub the student must wait for Bus 2, which is scheduled to depart at 0935. Bus 2 takes 1 h 18 min to reach School stop.
Set up: What are we solving for?
(i) At what time does Bus 1 arrive at Hub? 1 mark
(ii) How long does the student wait at Hub? 1 mark
(iii) At what time does the student arrive at School, and what is the total elapsed time of the whole journey? 3 marks
Stuck on total? Total = riding time on Bus 1 + wait + riding time on Bus 2 (or directly: depart City to arrive School).Problem 4, Long-haul flight with stopover (Sydney local time only)
A Sydney-to-Singapore-to-London flight, all times in Sydney local time:
Leg 1: depart Sydney 2215, flight time 8 h 25 min.
Stopover in Singapore: 1 h 50 min.
Leg 2: from end of stopover, flight time 13 h 15 min to London.
Set up: What are we solving for?
(i) What is the Sydney local time when the plane lands in Singapore? 2 marks
(ii) What is the Sydney local time when the plane departs Singapore? 1 mark
(iii) What is the total elapsed time from departure in Sydney to arrival in London (in h and min)? 2 marks
Stuck? Add the three durations (no time-zone conversion needed, all times kept in one frame).Problem 5, Reverse-engineer a deadline
Using the Sydney Trains Western Line timetable from Problem 1, a passenger needs to be at Penrith no later than 0915 for a job interview.
Set up: What are we solving for?
(i) List each service's arrival time at Penrith and decide which arrive at or before 0915. 1 mark
(ii) Which is the latest service the passenger can take from Central, and what time does that train depart Central? 2 marks
(iii) The passenger needs to leave home 25 minutes before the train departs Central. What is the latest time they can leave home? 2 marks
Stuck? Penrith arrivals are at 0830, 0901 and 0946, only the first two are at or before 0915.How did this worksheet feel?
What I'll revisit before next class:
Problem 1, Sydney Trains timetable
Set up. Subtract Central time from Penrith time per service, then compare A vs C.
(i) Service A: 0830 − 0717. Minutes: 30 − 17 = 13; hours: 8 − 7 = 1. Time = 1 h 13 min.
(ii) At Parramatta: Service A 0748 (gone), Service B 0819 (gone), Service C 0904 (next). Service C arrives Penrith at 0946 (9:46 am).
(iii) Service C: 0946 − 0832. Min: 46 − 32 = 14; hr: 9 − 8 = 1. Time = 1 h 14 min. Difference = 1 h 14 min − 1 h 13 min = 1 min longer.
Problem 2, Night shift
Set up. Convert both times to 24-hour, count up via midnight, then convert h–min to decimal hours and multiply by pay rate.
(i) 7:45 pm = 1945; 7:18 am = 0718.
(ii) 1945 → 0000 = 4 h 15 min; 0000 → 0718 = 7 h 18 min. Total = 11 h 33 min.
(iii) Decimal: 11 + 33/60 = 11 + 0.55 = 11.55 h. Pay = 11.55 × $42.60 = $492.03.
Problem 3, Connecting buses
Set up. Add ride time, then count to wait until next departure, then add ride time again. Verify total against single elapsed time City→School.
(i) Bus 1 arrives Hub at 0832 + 47 min: 32 + 47 = 79 = 1 h 19 → arrival = 0919.
(ii) Wait = 0935 − 0919 = 16 min.
(iii) Bus 2 departs Hub 0935, takes 1 h 18 min: 0935 + 1 h = 1035; + 18 min: 35 + 18 = 53 → arrives 1053. Total journey = 1053 − 0832: min 53 − 32 = 21; hr 10 − 8 = 2; total = 2 h 21 min. Check: 47 + 16 + 78 = 141 min = 2 h 21 min ✓.
Problem 4, Sydney–Singapore–London (Sydney time)
Set up. Three sequential durations; add to depart time and total.
(i) 2215 + 8 h 25 min: 2215 + 8 h = 0615 next day; + 25 min: 15 + 25 = 40 → arrives Singapore 0640 Sydney time.
(ii) Depart Singapore = 0640 + 1 h 50 = 0640 + 1 h = 0740; + 50 min: 40 + 50 = 90 = 1 h 30 → = 0830 Sydney time.
(iii) Total = 8 h 25 + 1 h 50 + 13 h 15. Min: 25 + 50 + 15 = 90 min = 1 h 30 min. Hr: 8 + 1 + 13 + 1 = 23. Total = 23 h 30 min.
Problem 5, Reverse-engineer to leave home
Set up. Find which services arrive Penrith ≤ 0915, take the latest one, subtract 25 min from its Central departure.
(i) Penrith arrivals: 0830 (A) ✓; 0901 (B) ✓; 0946 (C) ✗. Services A and B are both acceptable.
(ii) Latest is Service B, which departs Central at 0748.
(iii) Leave home = 0748 − 25 min: 48 − 25 = 23 → leave by 0723 (7:23 am).