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Time Calculations & Time Zones

Maths · Y8 Ratios & Rates
Year 8
Lesson Guide
Explanation
Timetables and airports use 24-hour time to abolish am/pm confusion. The conversion: pm hours add 12 (3:45 pm → 1545); hours of 13 or more subtract 12 and say pm (2130 → 9:30 pm). Always four digits — 7:05 am is 0705 — with midnight as 0000 and midday as 1200. The morning hours barely change; it's the afternoon that shifts by twelve.
Your Turn
Convert: 8:20 pm → 24-h, and 1408 → 12-h. Check: 2020; and 2:08 pm.
Watch Out
12-o-clock traps: 12:30 pm = 1230 (NOT 2430), and 12:30 am = 0030. The twelves break the add-12 rule — learn them as special cases.
Explanation
Elapsed time from 0935 to 1410: NEVER column-subtract clock times — 1410 − 0935 = '475' is gibberish because clocks carry at 60, not 100. Hop through friendly stones instead: 0935 → 1000 is 25 min, 1000 → 1400 is 4 h, 1400 → 1410 is 10 min. Total 4 h 35 min. The o'clocks are your stepping stones, exactly as in Year 3 — the numbers just got bigger.
Your Turn
Elapsed: 1147 to 1523? Check: 13 min → 1200, 3 h → 1500, 23 min → 3 h 36 min.
Watch Out
If you MUST subtract, borrow in sixties: 1410 − 0935 → borrow 1 h as 60 min: (13:70 − 9:35) = 4:35. Hopping is safer.
Explanation
Timetable craft at Y8: columns are services, rows are stations, dashes mean the train skips that stop. The express reaches Penrith in 46 minutes (0812→0858) versus 66 for the all-stops — but the express is useless if you need Strathfield. Connection questions chain the skills: arrive 0844, next express leaves 0858 → a 14-minute wait. Read down for a journey, across to compare, and mind the dashes.
Your Turn
You reach Parramatta at 0835. Which train gets you to Penrith, and when do you arrive? Check: missed the 0832 express — the all-stops at 0844, arriving 0921.
Watch Out
A train departing at your arrival minute is MISSED — you need strictly earlier arrival to make a connection.
Explanation
The Earth spins, so clocks differ by fixed OFFSETS from UTC: Perth +8, Adelaide +9½ (half-hour zones are real!), Sydney +10, Auckland +12. The gap between two places is the difference of their offsets: Sydney to Perth is 10 − 8 = 2 hours, with Perth BEHIND (west = earlier). At Sydney noon: Perth 10:00 am, Adelaide 11:30 am, Auckland 2:00 pm. East of you = later; west = earlier — the sun's daily journey in one rule.
Your Turn
Sydney is 3:30 pm. Time in Auckland (+12) and Perth (+8)? Check: 5:30 pm and 1:30 pm.
Watch Out
Subtract the OFFSETS, never add them: Sydney(+10) and London(+0 UTC) differ by 10 h, not 10+0 nonsense either way.
Explanation
Flight questions mix elapsed time with zone offsets — the golden rule is: work entirely in ONE zone, convert at the end. Sydney→Perth departing 0900, flying 5 h: on the Sydney clock it lands 1400; convert to Perth (−2 h) → 1200 local. The reverse trap: 'left Perth 1000, landed Sydney 1700' looks like 7 hours — but convert the departure first (1000 Perth = 1200 Sydney): the real flight is 5 h. Clock differences across zones are NOT durations until you align the zones.
Your Turn
Depart Auckland (+12) at 0800, fly 3 h to Sydney (+10). Local landing time? Check: 1100 Auckland clock → 0900 Sydney.
Watch Out
Never mix zones mid-calculation. Pick one city's clock, do all arithmetic there, translate once at the very end.
Explanation
Chapter 3 complete: ratios (one part is the bridge), scale drawings (multiply out, divide in, k2 for areas), rates (the unit rate referees every comparison), 24-hour time, elapsed-time hopping, and time zones with the one-zone rule. Notice the single thread: almost every skill reduced to 'scale down to ONE unit, then rebuild' — one part, one cm, one hour, one gram. That thread is proportional reasoning, and it's the spine of Year 8. Quiz and exercises!
Your Turn
Capstone: a 1:200,000 map shows a 4 cm road. You drive it at 80 km/h. How many minutes? Check: 8 km → 0.1 h → 6 minutes.
Watch Out
Multi-skill problems chain units: map cm → real km → hours → minutes. Write each unit down as you pass through it.
📌 Key Points — this lesson in a nutshell
  • pm adds 12 to the hour — except the twelves: 12:30 pm = 1230 and 12:30 am = 0030.
  • Elapsed time: hop through the o'clocks; never column-subtract clock times.
  • Timetables: a dash means the service skips that stop; connections need a strictly earlier arrival.
  • Time-zone gap = difference of the UTC offsets; east is later, west is earlier.
  • Flight problems: do all arithmetic in ONE zone, convert once at the very end.
Step 1: Introduction
Step 1 of 6
The clock without am/pm 12:00 am 0000 midnight 7:30 am 0730 morning 12:00 pm 1200 midday 3:45 pm 1545 afternoon 11:20 pm 2320 night Rule: pm times ADD 12 to the hour (3:45 pm → 15:45). Going back: hours 13+ SUBTRACT 12 and say pm (2130 → 9:30 pm). Always 4 digits: 7:05 am = 0705. Midnight = 0000, midday = 1200. Timetables, airports and the military use 24-h time to kill am/pm confusion.
From 0935 to 1410 0935 1000 1400 1410 25 min 4 h 10 min Hop through friendly stones: 25 min → 4 h → 10 min. Total: 4 h 35 min. Column subtraction 1410 − 0935 = "475" is GIBBERISH — clocks carry at 60, not 100. Hop; don't subtract.
Reading the train timetable Station Express All stops Central 0812 0815 Strathfield — 0829 Parramatta 0832 0844 Penrith 0858 0921 A dash (—) means the train SKIPS that station. Express to Penrith: 46 min. All-stops: 66 min. The express saves 20 min — unless you need Strathfield, where only the all-stops calls!
When it's noon in Sydney… Perth UTC+8 1000 Adelaide UTC+9½ 1130 Sydney UTC+10 1200 Auckland UTC+12 1400 Each zone is an OFFSET from UTC. The difference between two places is the difference of their offsets: Sydney(+10) − Perth(+8) = 2 h. Sydney noon → Perth 1000 (west = earlier). Auckland 1400 (east = later). Yes, half-hour zones exist: Adelaide is +9½!
Sydney → Perth, departing 0900 Flight time 5 h. Perth is 2 h BEHIND Sydney. Landing time in Perth? Work in ONE zone, convert at the end: Sydney clock: 0900 + 5 h = 1400 Sydney time. Convert: Perth = Sydney − 2 h = 1200. Lands at 1200 Perth time ✓ Reverse trap: "left Perth 1000, landed Sydney 1700 — flight time?" Convert FIRST (1000 Perth = 1200 Sydney) → flight = 5 h, not 7!
Chapter 3 complete 🧰 Ratios one part is the bridge Scale × out, ÷ in, k2 for area Rates unit rate = referee 24-h time pm adds 12 Elapsed hop the o-clocks Zones offsets, one-zone rule One thread runs through it all: scale to ONE unit, then rebuild. Quiz time!
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