Mr. Ward's Teaching Materials

082i - Problem Solving with Time Zones and Duration

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Lesson 82 — Problem Solving and Consolidation: Duration and Time Zones

Strand: Measurement | Descriptor: AC9M8M04 | Duration: 45 minutes

Learning Intentions

  • To apply duration and time-zone reasoning flexibly to unfamiliar, multi-step problems.
  • To use Polya’s problem-solving process to structure solutions to complex time-zone problems.

Success Criteria

I can:

  1. Solve multi-step problems that combine 24-hour time, elapsed duration, and time-zone conversion.
  2. Choose and justify a strategy (e.g. converting to a common reference time) for a given problem.
  3. Check whether a duration or arrival-time answer is reasonable in context.
  4. Communicate a full solution with clearly labelled working.

Warmup

(6 minutes — “Always, sometimes, never”, pairs)

Decide whether each statement is always, sometimes, or never true. Give a supporting example or counterexample.

  1. Flying east across time zones makes it seem, on paper, like you arrive later in the day than the hours you actually spent flying.
  2. A flight’s printed duration equals its arrival local time minus its departure local time.
  3. All places on the same line of longitude share the same time zone.
  4. Adding 24 hours to a 24-hour time returns the same time, one day later.

Answers: 1. Sometimes — true only when the flight crosses at least one time zone eastward; false for a flight that stays within a single zone. 2. Sometimes — true only if departure and arrival share the same time zone; otherwise the offset difference must be added or subtracted. 3. Never — zone boundaries follow political and administrative borders, not strict longitude (e.g. the whole of China uses a single time zone despite spanning roughly five geographic zones). 4. Always — 24-hour time is periodic with period 24 h.

Activities

Activity 1 — Refresher: the Common-reference Method (15 min)

Quick explicit recap, then paired practice.

I do (recap): A ferry departs a UTC+2 zone at 22:40 and takes 6 h 50 min to reach a UTC+4 zone. Find the local arrival time.

Pairs — practice set (share answers as a class):

  1. Depart a UTC−3 zone at 18:15; flight of 5 h 40 min; arrive in a UTC+1 zone. Find local arrival time.
  2. Depart Perth (UTC+8) at 23:05; flight of 4 h 15 min; arrive in Singapore (UTC+8). Find local arrival time.
  3. A broadcast begins at 07:00 in a UTC−6 zone. What is the UTC time?
  4. A parcel is scanned at 02:50 in a UTC+9 zone (Tokyo). What was the UTC time of the scan?

Activity 2 — Extended Applied Problem: the Journalist’s Itinerary (18 min)

Individually, then compare methods in pairs.

A journalist flies from Perth (UTC+8), departing at 23:55. The flight to Dubai (UTC+4) takes 11 h 5 min. She has a 2 h 40 min layover in Dubai, then flies to London (UTC+0), a flight of 7 h 20 min. Find the local time and date she lands in London, and her total door-to-door travel time, including the layover.

Socratic scaffolding:

PromptPurpose
Understand: what exactly are we asked to find?Two things — the local arrival time (and date, relative to departure) in London, and the total elapsed door-to-door time including the layover.
What information do you have?A departure time and zone, two flight durations, one layover duration, and each city’s UTC offset.
Devise a planConvert every event to a single reference (UTC), add the durations in sequence, then convert the final UTC time back to London’s local time.
Carry out the plan. After flight 1 (): (next day) UTC — Dubai local . Depart Dubai local , i.e. UTC . After flight 2 (): UTC London local (same UTC day).
Look back — is the arrival time sensible?Departing at 23:55 and travelling roughly 21 hours in total should plausibly land the following day — the date shift checks out.
Look back — is there a simpler check?Total travel time should equal flight 1 + layover + flight 2, added directly with no UTC conversion at all: . This matches the UTC-based calculation exactly. ✓

Answer: She lands in London at 13:00, the day after she departed Perth. Her total door-to-door travel time is 21 h 5 min.

Checks for Understanding

(6 minutes — exit ticket, collected)

  1. A call is placed from Perth (UTC+8) at 20:15 to a colleague in New York (UTC−5). What is the local time in New York?
  2. A ship departs Auckland (UTC+12) at 06:00 and, after 33 hours at sea, arrives in Fiji (UTC+12). State the local arrival time and how many days after departure it is.
  3. A livestream begins at 19:00 UTC. A viewer in Sydney (UTC+11, daylight saving) wants the local start time — state it and whether it is the same day or the next.
  4. Reasoning. Two flights each have exactly 8 hours of flying time. Flight A departs Perth (UTC+8) at 10:00 for Tokyo (UTC+9). Flight B departs Tokyo at 10:00 for Perth. Without full working, explain which flight shows a smaller gap between its departure and arrival clock readings, and why.

Answers: 1. UTC ; New York . 2. h day h, so arrival is , one day after departure. 3. Sydney , the next day. 4. Flight B — flying from Tokyo into Perth crosses into a zone 1 hour behind, subtracting an hour from the apparent clock gap (showing 7 h for an 8 h flight), whereas Flight A crosses into a zone 1 hour ahead, adding an hour on top (showing 9 h for an 8 h flight).

Common Misconceptions

MisconceptionHow to pre-empt it
The clock-time gap between departure and arrival always equals the true flight duration.Revisit the CFU Q4 reasoning: crossing into a “later” or “earlier” zone adds to or subtracts from the apparent gap.
A layover doesn’t need to be added separately once everything is in UTC.Model explicitly that a layover is real elapsed time and must be included in any total door-to-door duration.
If two cities share the same UTC offset, time zones can be ignored altogether.True for finding duration only — the local date must still be tracked carefully across midnight (see the Fiji example).
”Two days later” always means adding exactly 48 hours.Show that the actual gap depends on the time of day of both events, not a fixed 48-hour block.
Rounding minutes at an intermediate step doesn’t affect the final duration.Work an example where early rounding shifts the final answer by several minutes; always carry exact minutes throughout.

Enrichment — Competition-Style Problems

E1 (Kangaroo style). A broadcast airs simultaneously to listeners in four cities with UTC offsets , , and . If the broadcast airs at 21:00 UTC, find the sum of the four local clock hour-readings (24-hour time, taking any reading of 24 or more back into the – range).

Answer

Local reading : ; ; ; .

Sum .

E2 (AMC Junior style). Trip 1 has three legs of h , h and h , with no layovers. Trip 2 has two legs of h and h , plus a single -minute layover. Which trip takes longer overall, and by how many minutes?

Answer

Trip 1: min.

Trip 2: , plus the -minute layover min.

Trip 2 is longer, by minutes.

E3 (Challenge). A satellite call is placed from a research base at UTC−11 to a ship at UTC+11 — a 22-hour offset difference. The call is placed at 09:00 local time at the base and lasts 30 minutes. Find the local time the call ends on the ship, and state whether the ship’s calendar date differs from the base’s at the moment the call starts.

Answer

Base local , UTC . Ship local (next day). Adding the -minute call: ends at , the day after the base’s date.

Since the ship’s clock already reads a time on “the next day” at the very instant the base’s clock reads , the ship’s calendar date is one day ahead of the base’s when the call starts — a consequence of the huge -hour offset gap.

Homework

  1. A conference call is scheduled for 15:00 UTC. State the local start time in (a) Perth (UTC+8) (b) Sydney (UTC+11, daylight saving) (c) Los Angeles (UTC−7, daylight saving).
  2. A flight departs Brisbane (UTC+10) at 06:45 and takes 9 h 20 min to reach Singapore (UTC+8). Find the local arrival time and state whether it is the same day or the next.
  3. Ferry A departs at 14:20 (zone UTC+2) and takes 3 h 45 min, arriving in a UTC+3 zone. Ferry B departs at 09:10 (zone UTC+2) and takes 5 h 05 min, arriving in the same UTC+3 zone. Which ferry arrives first (local time), and by how much?
  4. A livestream starts at 18:00 in Tokyo (UTC+9) and lasts 2 h 30 min. Give the start and end times in UTC.
  5. Reasoning. Two Australian cities show a 2-hour clock gap for part of the year but a 3-hour gap for the rest of the year. Suggest which two cities these could be, and explain why the gap changes with the seasons.
  6. Challenge. A relay passes through five stations with equally spaced UTC offsets, starting at UTC−10 and ending at UTC+10. Find the offset of each of the three intermediate stations. If the relay takes exactly 2 real hours to complete from the first station to the last, find the difference between the first station’s starting clock reading and the last station’s finishing clock reading.

Answers: 1. (a) 23:00 (b) 02:00, next day (c) 08:00. 2. Local arrival , same day. 3. Ferry A arrives local; Ferry B arrives local — Ferry B arrives first, by 3 h 50 min. 4. UTC start , UTC end . 5. E.g. Perth (AWST, UTC+8, no daylight saving) and Sydney (AEST/AEDT) — the gap is h when Sydney is on standard time, widening to h once Sydney moves to AEDT in summer. 6. Offsets step by : . Clock-reading difference the -hour offset span hours of real elapsed time .

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