Mathematics Standard • Year 11 • Module 2 • Lesson 20

Timetables and Elapsed Time — Past-Paper Style

HSC Mathematics Standard 2-style writing: short-answer time conversions and elapsed-time calculations plus one extended response with explicit marking criteria.

Master · Past-Paper Style

1. Short-answer questions

1.1 A train departs at 9:48 pm and arrives at 1:23 am the next morning. Calculate the elapsed time of the journey in hours and minutes. Show all steps.    3 marks    Band 3

1.2 A bus timetable shows the following stops for one service.

Wynyard 0742; Town Hall 0748; Central 0755; Redfern 0801; Newtown 0810.

(a) How long does the bus take from Wynyard to Newtown?
(b) A passenger needs to arrive at Newtown by 0815. Is this service suitable? Explain in one sentence.    3 marks    Band 3–4

1.3 A pizza delivery driver is paid for two shifts in one day: 11:15 am to 2:48 pm, and again from 5:30 pm to 11:12 pm.
(a) Calculate the length (h, min) of each shift.
(b) Calculate the total hours worked across both shifts.
(c) The driver is paid $24.80 per hour. Calculate her total pay for the day.    4 marks    Band 4

Stuck on 1.3(c)? Convert total h–min to decimal hours before multiplying by the pay rate.

2. Extended response

2.1 A traveller is planning a trip from Newcastle to a regional town. The schedule is:

Leg 1: Train from Newcastle, departing at 6:42 pm, taking 2 h 38 min to Sydney Central.

Wait at Central: 47 min before catching the next service.

Leg 2: Overnight bus from Central, taking 7 h 15 min to the regional town.

The traveller has been told they must be at the destination by 8:00 am the next morning for a connecting work meeting.

(a) At what 24-hour time does the train arrive at Sydney Central?
(b) At what 24-hour time does the overnight bus depart Central?
(c) At what 24-hour time does the traveller arrive at the regional town?
(d) State whether the traveller arrives in time for the 8:00 am meeting, and by how many minutes they have to spare (or are late). Justify your answer in a sentence.    7 marks    Band 5–6

Explicit marking criteria

Part (a) — 2 marks

1 mark — converts 6:42 pm correctly to 1842.

1 mark — adds 2 h 38 min correctly to give 2120.

Part (b) — 1 mark

1 mark — adds 47 min to 2120 to give 2207.

Part (c) — 2 marks

1 mark — recognises midnight crossing and counts up via 0000 (or adds 2400 then subtracts).

1 mark — correct arrival 0522 next morning.

Part (d) — 2 marks

1 mark — correct difference between 0522 and 0800 in hours/minutes.

1 mark — clear sentence stating arrives in time, with a numerical buffer.

Your response:

Stuck on (c)? Bus departs 2207, takes 7 h 15. 2207 + 7 h = 2907 → 0507 next day; + 15 min = 0522 next day.

How did this worksheet feel?

What I'll revisit before next class:

Answers — sample responses + marking notes

1.1 — Elapsed time crossing midnight (3 marks)

Sample response.
Depart 9:48 pm = 2148; arrive 1:23 am = 0123.
Crosses midnight (0123 < 2148).
Count up: 2148 → 2200 = 12 min; 2200 → 0000 = 2 h; so 2148 → 0000 = 2 h 12 min.
Then 0000 → 0123 = 1 h 23 min.
Total elapsed = 2 h 12 min + 1 h 23 min = 3 h 35 min.

Marking notes. 1 mark — correct conversion of both times to 24-hour. 1 mark — correct midnight-crossing handling (count to midnight + count past midnight). 1 mark — correct final answer with h and min units. Common error: doing 0123 − 2148 directly gives a negative — must add 2400 first.

1.2 — Bus timetable (3 marks)

(a) Sample response. Newtown 0810 − Wynyard 0742 = 28 min.

(b) Sample response. 0810 is earlier than 0815, so yes — this service arrives 5 minutes before the deadline, with time to spare.

Marking notes. (a) 1 mark — correct elapsed minutes. (b) 1 mark — correct yes/no. 1 mark — sentence with a numerical buffer (5 min). A bare "yes" with no justification scores 1/2.

1.3 — Two shifts plus pay (4 marks)

(a) Sample response.
Shift 1: 11:15 am to 2:48 pm → 1115 to 1448. Min: 48 − 15 = 33; hr: 14 − 11 = 3 → 3 h 33 min.
Shift 2: 5:30 pm to 11:12 pm → 1730 to 2312. Min: 12 − 30 → borrow 1 h: 72 − 30 = 42; hr: 23 − 1 − 17 = 5 → 5 h 42 min.

(b) Sample response. Total min = 33 + 42 = 75 = 1 h 15 min. Total hr = 3 + 5 + 1 = 9 h 15 min. Total = 9 h 15 min.

(c) Sample response. Decimal: 9 + 15/60 = 9.25 h. Pay = 9.25 × $24.80 = $229.40.

Marking notes. (a) 1 mark — both shift lengths correct. (b) 1 mark — correct sum with carry of 60-minute overflow. (c) 1 mark — decimal conversion. 1 mark — correct dollar pay.

2.1 — Newcastle → regional town journey, sample Band-6 (7 marks)

Sample Band-6 response.

(a) Train arrival at Central.

6:42 pm = 1842. [1 mark.]
Add 2 h 38 min: 1842 + 2 h = 2042; + 38 min: 42 + 38 = 80 → 80 min = 1 h 20 min → 2042 + 1 h 20 min = 2200 + 20 min = 2120 (9:20 pm). [1 mark.]

(b) Bus departure from Central.

2120 + 47 min: 20 + 47 = 67 = 1 h 7 → 2120 + 1 h 7 min = 2207 (10:07 pm). [1 mark.]

(c) Bus arrival at destination.

2207 + 7 h 15 min. 2207 + 7 h = 2907; subtract 2400 (crosses midnight) → 0507 next day. [1 mark — midnight handled.]
Add 15 min: 0507 + 15 min = 0522 next morning. [1 mark.]

(d) Arrival vs deadline.

Deadline = 0800; arrival = 0522. Buffer = 0800 − 0522. Min: 0 − 22 → borrow 1 h: 60 − 22 = 38; hr: 7 − 1 − 5 = 2. Buffer = 2 h 38 min. [1 mark — correct difference.]

Conclusion: the traveller arrives at 0522, which is 2 h 38 min before the 8:00 am meeting — they have time to spare. [1 mark — clear conclusion with numerical buffer and direction.]

Total: 7/7.

Band descriptors for marker.

Band 3: Correct conversion of times to 24-hour and correct (a); struggles with the 38 min carry in (a) or omits (d) entirely. ≈ 3 marks.

Band 4: Parts (a)–(c) correct but slips on the midnight crossing in (c) (gives 2907 as the answer instead of 0522); (d) attempted but loses the conclusion mark. ≈ 4–5 marks.

Band 5: All numerical answers correct; (d) has the correct buffer but no conclusion sentence (bare "2 h 38 min"). ≈ 6 marks.

Band 6: Complete and correct, with all times in 24-hour, midnight handled cleanly, and a clear conclusion sentence in (d) that includes the buffer and the direction (early/late). 7/7.