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.

Apply · Problem Set

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:

Answers — Do not peek before attempting

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).