Mathematics Standard • Year 11 • Module 2 • Lesson 21
Time Zones and UTC — Problem Set
Apply UTC and time-zone reasoning to real scheduling problems: live broadcasts, international flights, sports, and business meetings spanning continents.
Problem 1 — Live broadcast from Tokyo
A live international event is broadcast from Tokyo at 8:30 pm local time (Japan Standard Time = UTC+9) on a Saturday.
Set up: What are we solving for?
(i) Convert the Tokyo broadcast time to UTC. 1 mark
(ii) At what local time should a Sydney viewer (AEDT = UTC+11, summer) tune in? 1 mark
(iii) At what local time should a New York viewer (EST = UTC−5) tune in? State the day in New York. 2 marks
Stuck? Always go local → UTC → other local. State day clearly when you cross midnight or the date line.Problem 2 — Sydney to London flight via Singapore
A flight departs Sydney at 11:50 pm Sunday AEDT (UTC+11). It flies 8 hours 25 minutes to Singapore (UTC+8), where it stops for 1 hour 30 minutes. It then flies 13 hours 50 minutes to London (UTC+0, winter — no BST).
Set up: What are we solving for?
(i) Convert Sydney departure to UTC. 1 mark
(ii) Find the UTC arrival time in Singapore. State the day. 2 marks
(iii) Find the local Singapore arrival time. Then add the layover and the second leg to find the UTC arrival in London, and convert to London local time. State the day in London. 3 marks
Stuck? Add elapsed times in UTC, then convert UTC to local at the end of each phase.Problem 3 — Three-way business call
A business call is to include three participants: Sydney (AEDT = UTC+11, summer), London (GMT = UTC+0, winter — no BST), and New York (EST = UTC−5, winter). The call must be at 9:00 am local time in London.
Set up: What are we solving for?
(i) What is 9:00 am London time in UTC? 1 mark
(ii) What local time must the Sydney participant join? State whether it is reasonable (e.g. within 7 am – 9 pm). 2 marks
(iii) What local time must the New York participant join? State the day in NY. 2 marks
Stuck on (iii)? UTC = 0900; NY = 0900 − 5 = 0400 — a very early start.Problem 4 — Tennis tournament viewing in different states
A tennis match in Melbourne (AEDT = UTC+11, summer) is scheduled to start at 7:30 pm local time on a Friday in January. Three fans want to watch:
Fan A in Brisbane (AEST = UTC+10, no DST).
Fan B in Perth (AWST = UTC+8, no DST).
Fan C in Auckland (NZDT = UTC+13, observes DST in January).
Set up: What are we solving for?
(i) Convert the Melbourne start time to UTC. 1 mark
(ii) Find the local start time for Fan A and Fan B. 2 marks
(iii) Find the local start time for Fan C in Auckland (state the day). 2 marks
Stuck? Auckland is ahead of Melbourne by 2 hours in January (UTC+13 vs UTC+11). Adding 2 hours to 1930 = 2130, still Friday.Problem 5 — Setting a Zoom call to suit Sydney
An exchange student in Singapore (UTC+8, no DST) and a friend in Sydney (AEST = UTC+10, July — no DST) want to schedule a Zoom meeting. They agree the Sydney friend will join at 7:30 pm local time.
Set up: What are we solving for?
(i) Convert Sydney's 7:30 pm to UTC. 1 mark
(ii) Find the corresponding local time in Singapore. 1 mark
(iii) The Singapore student says the meeting should be scheduled for a time that is 5:00 pm or later in Singapore so that it does not clash with their classes. Comment on whether the agreed time meets this constraint. 2 marks
(iv) If the call were instead to happen in January (Sydney now on AEDT = UTC+11), recompute Singapore's local time for the 7:30 pm Sydney slot. Does it still meet the constraint? 2 marks
Stuck? In July difference is 2 h (Sydney ahead); in January difference is 3 h (Sydney ahead).How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Tokyo broadcast
Set up. Tokyo local → UTC, then UTC → each viewer's local.
(i) Tokyo 2030 Sat − 9 = 1130 UTC Saturday.
(ii) Sydney AEDT = 1130 + 11 = 2230 Saturday (10:30 pm Sat).
(iii) New York EST = 1130 − 5 = 0630 Saturday (6:30 am Sat). Still Saturday in NY — no day rollover.
Problem 2 — Sydney–Singapore–London flight
Set up. Track every leg in UTC for clarity, then convert back to local at the points the question asks for.
(i) Sydney 2350 Sun − 11 = 1250 UTC Sunday.
(ii) UTC arrival Singapore = 1250 + 8 h 25 = 2115 Sunday. Singapore local = 2115 + 8 = 0515 UTC Mon… wait recompute: 1250 + 8 h = 2050; + 25 min = 2115 Sunday UTC. Hence UTC arrival Singapore = 2115 UTC Sunday.
(iii) Singapore local arrival = 2115 + 8 = 2915 → subtract 24 = 0515 Monday in Singapore.
UTC departure Singapore = 2115 + 1 h 30 = 2245 Sunday. UTC arrival London = 2245 + 13 h 50 = (2245 + 13 h = 3545 → 1145 Monday; + 50 min = 1235 Monday). UTC arrival London = 1235 Monday.
London local = UTC+0 → 1235 Monday in London (12:35 pm).
Problem 3 — Three-way call at 9 am London
Set up. Anchor on UTC, then radiate outward to Sydney and NY.
(i) London = UTC+0 → 0900 London = 0900 UTC.
(ii) Sydney AEDT = 0900 + 11 = 2000 (8:00 pm same day) — reasonable; sits within an evening window.
(iii) NY EST = 0900 − 5 = 0400 (4:00 am, same day in NY) — very early; participant would need an early start. Same calendar day as London.
Problem 4 — Tennis match viewing
Set up. Melbourne local → UTC, then add each fan's offset.
(i) Melbourne 1930 Fri AEDT − 11 = 0830 UTC Friday.
(ii) Fan A (Brisbane UTC+10) = 0830 + 10 = 1830 Friday (6:30 pm). Fan B (Perth UTC+8) = 0830 + 8 = 1630 Friday (4:30 pm).
(iii) Fan C (Auckland UTC+13) = 0830 + 13 = 2130 → still Friday in NZ → 9:30 pm Friday. (Auckland is 2 h ahead of Melbourne in January.)
Problem 5 — Singapore/Sydney Zoom call
Set up. Sydney → UTC → Singapore for each season; then check the 5:00 pm constraint.
(i) Sydney 1930 AEST − 10 = 0930 UTC.
(ii) Singapore = 0930 + 8 = 1730 (5:30 pm).
(iii) 1730 is after 1700, so the agreed time does meet the 5 pm constraint.
(iv) January: Sydney 1930 AEDT − 11 = 0830 UTC; Singapore = 0830 + 8 = 1630 (4:30 pm). This is before 5 pm → does NOT meet the constraint. The pair would need to push the Sydney time later by at least 30 minutes during summer.