Time and Location

Time and location was worth about 3 marks in the sample HSC paper. The questions are usually short and practical: a flight between countries, a phone call across Australia, or the time difference between two places on a map.

• Latitude and longitude: describe a position on the Earth's surface, with and without digital tools.
• 15° = 1 hour: calculate time differences from longitude.
• Convert between seconds, minutes and hours.
• Convert between 12-hour and 24-hour time.
• Calculate elapsed time, including across midnight.
• Australian time zones and daylight saving.
• UTC (Coordinated Universal Time): represent time differences and solve travel problems.

A position on Earth is given by two angles.

• Latitude measures how far north or south of the Equator (0°) a place is, up to 90°N or 90°S at the poles. Lines of latitude are called parallels.
• Longitude measures how far east or west of the Prime Meridian (0°, through Greenwich in London) a place is, up to 180°E or 180°W. Lines of longitude are called meridians and run from pole to pole.

Write latitude first, then longitude: Sydney is about (34°S, 151°E). Every place in Australia is south of the Equator and east of the Prime Meridian, so its coordinates are °S and °E. Mapping apps show coordinates as decimals, with negative numbers for south and west, so Sydney appears as about −33.9, 151.2.

The Earth turns 360° in 24 hours, so it turns 15° every hour:

To find the time difference between two places:

1. Find the difference in longitude. If both are east (or both west), subtract. If one is east and one is west, add.
2. Divide by 15 to get hours (or multiply by 4 to get minutes).
3. The place further east is ahead in time.

Worked example: time difference from longitude

Brisbane is at about 153°E and Cape Town is at about 18°E. Using longitude, find the time difference, and the time in Cape Town when it is 4 pm in Brisbane.

Brisbane is further east, so it is 9 hours ahead. When it is 4 pm in Brisbane, it is 7 am the same day in Cape Town.

This gives the theoretical difference. Real clocks follow time zones set by governments, which don't exactly match the meridians, so when a question gives UTC offsets, use those instead.

Units of time

1 minute = 60 seconds, 1 hour = 60 minutes = 3600 seconds. A decimal hour must be converted: 2.35 hours is 2 hours and $0.35\times 60=21$ minutes, so 2 h 21 min. Going the other way, 45 minutes is $\frac{45}{60}=0.75$ hours. The degrees-minutes-seconds key on a calculator converts in both directions.

12-hour and 24-hour time

24-hour time uses four digits with no am or pm. From 1 pm onwards, add 12 to the hour.

Midnight is 0000 and noon is 1200. Timetables and flight schedules use 24-hour time.

Elapsed time

Elapsed time is how long something takes. Count up in easy steps rather than subtracting clock times. From 9:45 pm to 6:20 am the next day: 9:45 pm to midnight is 2 h 15 min, and midnight to 6:20 am is 6 h 20 min, so the total is 8 h 35 min.

Australia's three main time zones, in standard time, are:

Daylight saving puts clocks forward 1 hour from the first Sunday in October to the first Sunday in April. NSW, the ACT, Victoria, Tasmania and South Australia use it; Queensland, the Northern Territory and Western Australia do not. So in summer:

• NSW, ACT, Vic and Tas are UTC+11 (AEDT).
• SA is UTC+10:30.
• Qld stays UTC+10, NT UTC+9:30 and WA UTC+8.

Example. In January, a student in Perth makes a video call at 7:30 pm Perth time. Sydney (UTC+11) is 3 hours ahead, so it is 10:30 pm there. In Brisbane (UTC+10) it is 9:30 pm, in Adelaide (UTC+10:30) 10:00 pm, and in Darwin (UTC+9:30) 9:00 pm.

Coordinated Universal Time (UTC) is the world reference time, equal to the standard time at 0° longitude. Each place is described by its offset, such as UTC+10 or UTC−5. To compare two places, subtract their offsets: Sydney in standard time (UTC+10) is $10-(-5)=15$ hours ahead of a place at UTC−5.

For a flight question, a reliable method is:

1. Write the departure time in the departure city's time.
2. Add the flight time to get the arrival time in the departure city's time.
3. Convert that to the arrival city's time using the difference in UTC offsets.

Worked example: a long-haul flight

A flight leaves Melbourne at 10:20 am on Tuesday during daylight saving (UTC+11). The flight takes 14 hours 25 minutes. Dubai is at UTC+4. Find the local time in Dubai when the plane lands.

Step 1 and 2: add the flight time in Melbourne time.

Step 3: Dubai is $11-4=7$ hours behind Melbourne.

The plane lands at 5:45 pm on Tuesday, Dubai time, the same day it left Melbourne. Check that the answer is sensible: travelling west, you "gain" hours, so the local arrival time is much earlier than 14 hours after departure.

Crossing the International Date Line (roughly the 180° meridian) changes the date. Going east across it (for example Australia to the USA) you go back a day; going west you go forward a day. Using UTC offsets handles this for you, as long as you track the day carefully.

• Subtracting longitudes when one is east and one is west. Add them.
• Getting the direction wrong. East is ahead, west is behind.
• Writing 2.35 hours as 2 h 35 min.
• Forgetting daylight saving, or applying it to Queensland, WA or the NT.
• Adding the flight time to the arrival city's time instead of the departure city's time.
• Losing track of the day when the time passes midnight.

• Set out travel questions in the three steps above, with the day written next to every time.
• When the question gives UTC offsets or a time zone map, use those, not the 15° rule. Use the 15° rule only when the question asks you to work from longitude.
• Answer with the time, am or pm (or 24-hour), and the day, in the time zone asked for.
• In describe questions about position, give latitude and longitude with N, S, E or W.

• Formulas and equations: speed, distance and time calculations use the same time conversions.
• Ratios and rates (Year 12): rates such as km/h depend on converting between hours and minutes.
• Trigonometry (Year 12): bearings describe direction on a smaller scale.
• Critical path analysis (Year 12): scheduling tasks also involves careful time arithmetic.