Year 11 · Measurement
Quick tips — memory joggers
12- & 24-hour time
Longitude & time
Time zones & UTC
Date Line & timetables
Level 1 · Fluency
In the coordinates (\(34^{\circ}\)S, \(151^{\circ}\)E), which value is the latitude?
\(34^{\circ}\)S is the latitude (angle north/south of the equator); \(151^{\circ}\)E is the longitude.
In the coordinates (\(48^{\circ}\)N, \(2^{\circ}\)E), which value is the longitude?
\(2^{\circ}\)E is the longitude (angle east/west of the Prime Meridian); \(48^{\circ}\)N is the latitude.
In the coordinates (\(23^{\circ}\)S, \(43^{\circ}\)W), which value is the latitude?
\(23^{\circ}\)S is the latitude (angle north/south of the equator); \(43^{\circ}\)W is the longitude.
Level 2 · Application
A city is described as being at \(40^{\circ}\)N, \(74^{\circ}\)W. State on which side of the equator and which side of the Prime Meridian it lies.
\(40^{\circ}\)N is north of the equator; \(74^{\circ}\)W is west of the Prime Meridian.
A town is at \(35^{\circ}\)S, \(20^{\circ}\)E. State on which side of the equator and which side of the Prime Meridian it lies.
\(35^{\circ}\)S is south of the equator; \(20^{\circ}\)E is east of the Prime Meridian.
A city is at \(60^{\circ}\)N, \(25^{\circ}\)E. State on which side of the equator and which side of the Prime Meridian it lies.
\(60^{\circ}\)N is north of the equator; \(25^{\circ}\)E is east of the Prime Meridian.
Level 3 · Further Application
Two cities are at (\(58^{\circ}\)N, \(16^{\circ}\)E) and (\(33^{\circ}\)S, \(151^{\circ}\)E).
(a) One is \(58^{\circ}\) north and the other \(33^{\circ}\) south, so the latitude difference \(= 58 + 33 = 91^{\circ}\).
(b) Both are east of the Prime Meridian: \(151 - 16 = 135^{\circ}\).
Two cities are at (\(45^{\circ}\)N, \(9^{\circ}\)E) and (\(12^{\circ}\)S, \(77^{\circ}\)W).
(a) \(57^{\circ}\); (b) \(86^{\circ}\)
(a) One is \(45^{\circ}\) north, the other \(12^{\circ}\) south, so latitude difference \(= 45 + 12 =\) \(57^{\circ}\).
(b) One is east and the other west of the Prime Meridian, so add: \(9 + 77 =\) \(86^{\circ}\).
Two cities are at (\(55^{\circ}\)N, \(37^{\circ}\)E) and (\(1^{\circ}\)S, \(36^{\circ}\)E).
(a) \(56^{\circ}\); (b) \(1^{\circ}\)
(a) One is \(55^{\circ}\) north, the other \(1^{\circ}\) south, so latitude difference \(= 55 + 1 =\) \(56^{\circ}\).
(b) Both are east of the Prime Meridian: \(37 - 36 =\) \(1^{\circ}\).
Level 1 · Fluency
On a globe, lines of latitude run in which direction — east–west or north–south?
East–west (they are parallel to the equator).
On a globe, lines of longitude (meridians) run in which direction — east–west or north–south?
North–south (they run from pole to pole).
The equator is the line of latitude at what value?
\(0^{\circ}\) — it is the line of latitude midway between the poles.
Level 2 · Application
Explain how longitude lines are used to measure position east or west.
Longitude lines (meridians) run north–south and are measured in degrees east or west of the Prime Meridian (\(0^{\circ}\)), up to \(180^{\circ}\).
Explain how latitude lines are used to measure position north or south.
Latitude lines run east–west and are measured in degrees north or south of the equator (\(0^{\circ}\)), up to \(90^{\circ}\) at each pole.
A smartphone GPS reads \(33.87^{\circ}\)S, \(151.21^{\circ}\)E. Explain what each number represents.
\(33.87^{\circ}\)S is the latitude — the angle south of the equator. \(151.21^{\circ}\)E is the longitude — the angle east of the Prime Meridian.
Level 3 · Further Application
A ship reports its position as \(23.5^{\circ}\)S, \(43^{\circ}\)W.
(a) Southern hemisphere and western hemisphere.
(b) Both ships are on the same line of latitude (\(23.5^{\circ}\)S), so they are the same distance south of the equator.
A plane reports its position as \(40^{\circ}\)N, \(116^{\circ}\)E.
(a) Northern hemisphere and eastern hemisphere.
(b) Both planes are on the same line of latitude (\(40^{\circ}\)N), so they are the same distance north of the equator.
A GPS reads \(19^{\circ}\)N, \(99^{\circ}\)W.
(a) Northern hemisphere and western hemisphere.
(b) Both points share the same longitude (\(99^{\circ}\)W), so they lie on the same meridian; the second is the same distance south of the equator as the first is north.
Level 1 · Fluency
The Earth turns \(15^{\circ}\) of longitude in how much time?
1 hour (\(360^{\circ} \div 24\) hours \(= 15^{\circ}\) per hour).
The Earth turns through \(360^{\circ}\) of longitude in how many hours?
24 hours (one full rotation is one day).
How many degrees of longitude does the Earth turn through in 1 hour?
\(15^{\circ}\)
\(360^{\circ} \div 24 =\) \(15^{\circ}\) per hour.
Level 2 · Application
Two places differ by \(45^{\circ}\) of longitude. Using \(15^{\circ} = 1\) hour, calculate the time difference between them.
3 hours
\(45 \div 15 =\) 3 hours.
Two places differ by \(60^{\circ}\) of longitude. Using \(15^{\circ} = 1\) hour, calculate the time difference between them.
4 hours
\(60 \div 15 =\) 4 hours.
Two places differ by \(120^{\circ}\) of longitude. Using \(15^{\circ} = 1\) hour, calculate the time difference between them.
8 hours
\(120 \div 15 =\) 8 hours.
Level 3 · Further Application
City A is at \(16^{\circ}\)E and City B is at \(151^{\circ}\)E.
(a) \(151 - 16 = 135^{\circ}\).
(b) \(135 \div 15 = 9\) hours. City B (further east) is 9 hours ahead of City A.
City A is at \(25^{\circ}\)W and City B is at \(50^{\circ}\)E.
(a) \(75^{\circ}\); (b) 5 hours, City B ahead
(a) The cities are on opposite sides of the Prime Meridian, so add: \(25 + 50 =\) \(75^{\circ}\).
(b) \(75 \div 15 = 5\) hours. City B (further east) is 5 hours ahead of City A.
City A is at \(100^{\circ}\)W and City B is at \(20^{\circ}\)W.
(a) \(80^{\circ}\); (b) 5 h 20 min, City B ahead
(a) Both are west of the Prime Meridian, so subtract: \(100 - 20 =\) \(80^{\circ}\).
(b) \(80 \div 15 = 5\tfrac{1}{3}\) hours \(= 5\) h \(20\) min. City B (further east) is 5 h 20 min ahead of City A.
Level 1 · Fluency
If a city is 3 hours ahead of you and it is 2:00 pm where you are, what time is it there?
5:00 pm
2:00 pm + 3 hours = 5:00 pm.
If a city is 4 hours behind you and it is 1:00 pm where you are, what time is it there?
9:00 am
1:00 pm − 4 hours = 9:00 am.
If a city is 2 hours ahead of you and it is 11:00 am where you are, what time is it there?
1:00 pm
11:00 am + 2 hours = 1:00 pm.
Level 2 · Application
Sydney is 9 hours ahead of a European city. When it is 5:00 pm Thursday in the European city, find the time and day in Sydney.
2:00 am Friday
5:00 pm + 9 hours = 2:00 am, and the extra hours cross midnight, so it is 2:00 am Friday in Sydney.
A city is 7 hours behind Sydney. When it is 6:00 am Monday in Sydney, find the time and day in that city.
11:00 pm Sunday
6:00 am − 7 hours = 11:00 pm, and subtracting crosses back over midnight, so it is 11:00 pm Sunday in that city.
City B is 5 hours ahead of City A. When it is 10:00 pm Tuesday in City A, find the time and day in City B.
3:00 am Wednesday
10:00 pm + 5 hours = 3:00 am, crossing midnight, so it is 3:00 am Wednesday in City B.
Level 3 · Further Application
A meeting is set for 5:00 pm Thursday, local time, in a city that is 9 hours behind Sydney.
2:00 am Friday
(a) Sydney is 9 hours ahead: 5:00 pm + 9 = 2:00 am the next day → 2:00 am Friday in Sydney.
(b) No — 2:00 am is the middle of the night, not work hours.
A conference begins at 9:00 am Monday, local time, in a city that is 8 hours behind Sydney.
5:00 pm Monday
(a) Sydney is 8 hours ahead: 9:00 am + 8 = 5:00 pm Monday in Sydney.
(b) Yes — 5:00 pm is at the end of the working day, so it is reasonable.
An event begins at 11:00 pm Saturday, local time, in a city that is 6 hours ahead of Sydney.
5:00 pm Saturday
(a) Sydney is 6 hours behind: 11:00 pm − 6 = 5:00 pm Saturday in Sydney.
(b) Yes — 5:00 pm is late afternoon, so it is during daytime.
Level 1 · Fluency
Write 7:45 pm in 24-hour time.
1945
1945 (add 12 to the hours after noon).
Write 6:20 am in 24-hour time.
0620
Morning times keep the same hours and are written with 4 digits: 0620.
Write 2350 in 12-hour time.
11:50 pm
Hours are past noon, so subtract 12: \(23 - 12 = 11\), giving 11:50 pm.
Level 2 · Application
A movie starts at 1830 and finishes at 2115. Calculate its length.
From 1830 to 2115 is 2 hours 45 minutes.
A class runs from 0925 to 1110. Calculate its length.
1 hour 45 minutes
0925 → 1025 is 1 hour; 1025 → 1110 is 45 minutes; total = 1 h 45 min.
A shift starts at 1345 and ends at 1720. Calculate its length.
3 hours 35 minutes
1345 → 1645 is 3 hours; 1645 → 1720 is 35 minutes; total = 3 h 35 min.
Level 3 · Further Application
A flight departs at 2245 and lands at 0620 the next day (same time zone).
7 h 35 min; 6:20 am
(a) 2245 → 2400 is 1 h 15 min; 0000 → 0620 is 6 h 20 min; total = 7 h 35 min.
(b) 0620 = 6:20 am.
A train departs at 2330 and arrives at 0505 the next day (same time zone).
5 h 35 min; 5:05 am
(a) 2330 → 2400 is 30 min; 0000 → 0505 is 5 h 5 min; total = 5 h 35 min.
(b) 0505 = 5:05 am.
A bus departs at 2140 and arrives at 0015 the next day (same time zone).
2 h 35 min; 9:40 pm
(a) 2140 → 2400 is 2 h 20 min; 0000 → 0015 is 15 min; total = 2 h 35 min.
(b) 2140 = 9:40 pm (\(21 - 12 = 9\)).
Level 1 · Fluency
Places to the east see the sun earlier, so their local time is ahead or behind?
Ahead — eastern places are ahead in time.
Places to the west see the sun later, so their local time is ahead or behind?
Behind — western places are behind in time.
Moving to a place further east, do you add or subtract time from your local time?
Add — east is ahead, so add the time difference.
Level 2 · Application
Town P is at \(30^{\circ}\)E and Town Q is at \(105^{\circ}\)E. Calculate the time difference and state which is ahead.
Longitude difference \(= 105 - 30 = 75^{\circ}\); \(75 \div 15 = 5\) hours. Town Q (further east) is 5 hours ahead.
Town M is at \(40^{\circ}\)W and Town N is at \(20^{\circ}\)E. Calculate the time difference and state which is ahead.
4 hours; Town N ahead
Opposite sides of the Prime Meridian, so add: \(40 + 20 = 60^{\circ}\); \(60 \div 15 = 4\) hours. Town N (further east) is 4 hours ahead.
Town R is at \(140^{\circ}\)E and Town S is at \(95^{\circ}\)E. Calculate the time difference and state which is ahead.
3 hours; Town R ahead
Same side, so subtract: \(140 - 95 = 45^{\circ}\); \(45 \div 15 = 3\) hours. Town R (further east) is 3 hours ahead.
Level 3 · Further Application
It is 9:00 am at a town on \(20^{\circ}\)E.
2:00 pm; 7:00 am
(a) Difference \(= 75^{\circ} = 5\) hours east ⇒ 9:00 am + 5 = 2:00 pm.
(b) Difference \(= 30^{\circ} = 2\) hours west ⇒ 9:00 am − 2 = 7:00 am.
It is 10:00 am at a town on \(15^{\circ}\)E.
1:00 pm; 7:00 am
(a) Difference \(= 60 - 15 = 45^{\circ} = 3\) hours east ⇒ 10:00 am + 3 = 1:00 pm.
(b) Difference \(= 15 + 30 = 45^{\circ} = 3\) hours west ⇒ 10:00 am − 3 = 7:00 am.
It is 3:00 pm at a town on \(45^{\circ}\)E.
6:00 pm; 12:00 pm (noon)
(a) Difference \(= 90 - 45 = 45^{\circ} = 3\) hours east ⇒ 3:00 pm + 3 = 6:00 pm.
(b) Difference \(= 45^{\circ} = 3\) hours west ⇒ 3:00 pm − 3 = 12:00 pm (noon).
Level 1 · Fluency
Australian Eastern Standard Time (AEST) is UTC +10. During daylight saving (AEDT), what is the offset?
UTC +11 (clocks go forward one hour).
Perth (AWST) is UTC +8. How many hours behind AEST (UTC +10) is Perth?
2 hours behind (\(10 - 8 = 2\)).
When daylight saving begins in spring, do the clocks go forward or back, and by how much?
Forward by one hour.
Level 2 · Application
Perth is UTC +8 and Sydney is UTC +10 (no daylight saving). When it is 3:00 pm in Perth, find the time in Sydney.
5:00 pm
Sydney is 2 hours ahead: 3:00 pm + 2 = 5:00 pm.
Adelaide is UTC +9:30 and Sydney is UTC +10 (no daylight saving). When it is 2:00 pm in Adelaide, find the time in Sydney.
2:30 pm
Sydney is \(10 - 9.5 = 0.5\) hour ahead: 2:00 pm + 30 min = 2:30 pm.
Brisbane is UTC +10 and Darwin is UTC +9:30 (no daylight saving). When it is 6:00 pm in Brisbane, find the time in Darwin.
5:30 pm
Darwin is \(10 - 9.5 = 0.5\) hour behind: 6:00 pm − 30 min = 5:30 pm.
Level 3 · Further Application
In summer, Sydney observes daylight saving (UTC +11) but Brisbane does not (UTC +10).
7:30 pm
(a) 1 hour (Sydney is ahead).
(b) Brisbane is 1 hour behind: 8:30 pm − 1 = 7:30 pm.
In summer, Melbourne observes daylight saving (UTC +11) but Brisbane does not (UTC +10).
6:45 pm
(a) 1 hour (Melbourne is ahead).
(b) Brisbane is 1 hour behind: 7:45 pm − 1 = 6:45 pm.
In summer, Adelaide observes daylight saving (UTC +10:30) but Perth does not (UTC +8).
7:30 pm
(a) \(10.5 - 8 = 2.5\) hours (Adelaide is ahead).
(b) 5:00 pm + 2 h 30 min = 7:30 pm.
Level 1 · Fluency
UTC +10 means the local time is how many hours ahead of UTC?
10 hours ahead.
UTC −5 means the local time is how many hours behind UTC?
5 hours behind.
What is the UTC offset of a place on the Prime Meridian keeping standard time?
UTC +0 (its local time equals UTC).
Level 2 · Application
A city is UTC −5. When it is 1200 UTC, find the local time in that city.
7:00 am
12:00 − 5 hours = 7:00 am local time.
A city is UTC +7. When it is 1000 UTC, find the local time in that city.
5:00 pm
10:00 + 7 hours = 1700 = 5:00 pm local time.
A city is UTC −3. When it is 0100 UTC, find the local time and day in that city.
10:00 pm the previous day
0100 − 3 hours = 2200 the day before, so it is 10:00 pm the previous day.
Level 3 · Further Application
A traveller flies east across the International Date Line.
(a) The date goes back by one day (you subtract a day) when crossing the Date Line travelling east.
(b) It provides an agreed line where the calendar date changes, so that time zones going east and west around the globe meet consistently.
A traveller flies west across the International Date Line.
(a) The date moves forward by one day (you add a day) when crossing the Date Line travelling west.
(b) It runs roughly along the \(180^{\circ}\) meridian in the Pacific Ocean, opposite the Prime Meridian.
A ship crosses the Date Line between a zone at UTC +12 and a zone at UTC −12.
(a) The clocks read the same hour and minute, but the calendar dates differ by one day (the +12 side is one day ahead of the −12 side).
(b) They lie on opposite sides of the \(180^{\circ}\) meridian, which is 12 hours (\(180 \div 15\)) from UTC in each direction.
Level 1 · Fluency
London is UTC +0 and Sydney is UTC +10. How many hours ahead is Sydney?
10 hours.
Paris is UTC +1 and Sydney is UTC +10. How many hours ahead is Sydney?
9 hours (\(10 - 1 = 9\)).
New York is UTC −5 and London is UTC +0. How many hours ahead is London?
5 hours (\(0 - (-5) = 5\)).
Level 2 · Application
Tokyo is UTC +9 and Los Angeles is UTC −8. Calculate the time difference between them.
17 hours
\(9 - (-8) =\) 17 hours (Tokyo ahead of Los Angeles).
Dubai is UTC +4 and New York is UTC −5. Calculate the time difference between them.
9 hours
\(4 - (-5) =\) 9 hours (Dubai ahead of New York).
Sydney is UTC +10 and Los Angeles is UTC −8. Calculate the time difference between them.
18 hours
\(10 - (-8) =\) 18 hours (Sydney ahead of Los Angeles).
Level 3 · Further Application
New York is UTC −5 and Sydney is UTC +11 (summer).
1:00 am Tuesday
(a) \(11 - (-5) = 16\) hours (Sydney ahead).
(b) 9:00 am + 16 = 1:00 am the next day → 1:00 am Tuesday in Sydney.
London is UTC +0 and Tokyo is UTC +9.
5:00 am Tuesday
(a) \(9 - 0 = 9\) hours (Tokyo ahead).
(b) 8:00 pm + 9 = 5:00 am the next day → 5:00 am Tuesday in Tokyo.
Los Angeles is UTC −8 and Sydney is UTC +11 (summer).
10:00 am Monday
(a) \(11 - (-8) = 19\) hours (Sydney ahead).
(b) 3:00 pm + 19 h = 10:00 am the next day → 10:00 am Monday in Sydney.
Level 1 · Fluency
A bus timetable lists a departure at 0815 and the next at 0850. How often do buses leave?
Every 35 minutes.
A train timetable lists a departure at 0710 and the next at 0755. How often do trains leave?
Every 45 minutes.
A ferry timetable lists a departure at 1120 and the next at 1140. How often do ferries leave?
Every 20 minutes.
Level 2 · Application
A train departs Central at 1742 and arrives at the destination at 1826. Calculate the journey time.
1742 → 1826 = 44 minutes.
A bus departs at 0938 and arrives at the terminus at 1015. Calculate the journey time.
37 minutes
0938 → 1000 is 22 min; 1000 → 1015 is 15 min; total = 37 minutes.
A train departs at 1450 and arrives at the destination at 1533. Calculate the journey time.
43 minutes
1450 → 1500 is 10 min; 1500 → 1533 is 33 min; total = 43 minutes.
Level 3 · Further Application
A ferry leaves at 0910 and takes 25 minutes. A connecting bus departs the wharf every 20 minutes from 0900.
0940
(a) 0910 + 25 min = 0935.
(b) Buses leave at 0900, 0920, 0940 …; the earliest after 0935 is 0940, a wait of 5 minutes.
A ferry leaves at 1045 and takes 35 minutes. A connecting train departs the wharf every 15 minutes from 1030.
1130, wait 10 minutes
(a) 1045 + 35 min = 1120.
(b) Trains leave at 1030, 1045, 1100, 1115, 1130 …; the earliest after 1120 is 1130, a wait of 10 minutes.
A bus leaves at 1335 and takes 50 minutes. A connecting tram departs the interchange every 12 minutes from 1400.
1436, wait 11 minutes
(a) 1335 + 50 min = 1425.
(b) Trams leave at 1400, 1412, 1424, 1436 …; the earliest after 1425 is 1436, a wait of 11 minutes.
Level 1 · Fluency
A live match starts at 8:00 pm in a city that is 3 hours behind you. What time does it start where you are?
11:00 pm
8:00 pm + 3 = 11:00 pm.
A concert streams at 7:00 pm in a city that is 2 hours ahead of you. What time does it start where you are?
5:00 pm
The other city is ahead, so subtract: 7:00 pm − 2 = 5:00 pm.
A game starts at 6:00 pm in a city that is 4 hours behind you. What time does it start where you are?
10:00 pm
The other city is behind, so add: 6:00 pm + 4 = 10:00 pm.
Level 2 · Application
A person in Sydney (UTC +10) wants to call a friend in London (UTC +0) at 9:00 am London time. Find the time to call in Sydney.
7:00 pm
Sydney is 10 hours ahead: 9:00 am + 10 = 7:00 pm in Sydney.
A person in Sydney (UTC +10) wants to call a friend in New York (UTC −5) at 8:00 am New York time. Find the time to call in Sydney.
11:00 pm
Difference \(= 10 - (-5) = 15\) hours (Sydney ahead): 8:00 am + 15 = 11:00 pm in Sydney.
A person in Perth (UTC +8) wants to join a meeting at 10:00 am Tokyo time (UTC +9). Find the time to join in Perth.
9:00 am
Tokyo is \(9 - 8 = 1\) hour ahead, so Perth is 1 hour behind: 10:00 am − 1 = 9:00 am in Perth.
Level 3 · Further Application
A webinar is broadcast live at 2:00 pm Wednesday in a city that is UTC −5. A viewer is in Sydney (UTC +11, summer).
6:00 am Thursday
(a) \(11 - (-5) = 16\) hours (Sydney ahead).
(b) 2:00 pm Wednesday + 16 h = 6:00 am the next day → 6:00 am Thursday in Sydney.
A live final airs at 8:00 pm Saturday in a city that is UTC −4. A fan is in Sydney (UTC +11, summer).
11:00 am Sunday
(a) \(11 - (-4) = 15\) hours (Sydney ahead).
(b) 8:00 pm Saturday + 15 h = 11:00 am the next day → 11:00 am Sunday in Sydney.
A product launch streams live at 10:00 am Monday in a city that is UTC +1. A viewer is in Sydney (UTC +11, summer).
8:00 pm Monday
(a) \(11 - 1 = 10\) hours (Sydney ahead).
(b) 10:00 am Monday + 10 h = 8:00 pm Monday in Sydney.