Every place on Earth can be pinpointed with just two numbers. Latitude tells you how far north or south of the equator; longitude tells you how far east or west — and longitude directly determines your local time.
55–60 minMS-M3 — NEW 20243 MC3 SALesson 22 of 22Free
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The Earth takes 24 hours to complete a full 360° rotation. That means the Sun appears to move 15° of longitude every hour. Sydney is at roughly 151°E longitude. If noon (the Sun directly overhead) occurs at 0° longitude at some moment, how long does it take for noon to reach Sydney? What does this tell you about why Sydney's time should be roughly UTC+10?
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Latitude and Longitude Formulas — This Lesson
Rate $= \dfrac{360°}{24 \text{ h}} = 15° \text{ per hour}$
The Earth rotates through 360° in 24 hoursEvery 15° of longitude = 1 hour of time differenceEvery 1° of longitude = 4 minutes of time difference
Time difference (h) $= \dfrac{\Delta \lambda}{15}$
$\Delta \lambda$ (delta lambda) — difference in longitude in degreesEast of reference = ahead in time; West = behinde.g. $\Delta\lambda = 135°$ → time difference $= 135 \div 15 = 9$ hours
Coordinates: (latitude°N/S, longitude°E/W)
Latitude: 0° = equator; 90°N = North Pole; 90°S = South PoleLongitude: 0° = Prime Meridian (Greenwich); 180° = International Date Linee.g. Sydney ≈ (33.9°S, 151.2°E); London ≈ (51.5°N, 0.1°W)
🧠 Know
Latitude measures north/south position; longitude measures east/west position
Equator = 0° lat; Prime Meridian = 0° long
Earth rotates 360° in 24 h → 15° per hour; 1° = 4 minutes
East longitudes are ahead of UTC; west longitudes are behind
💡 Understand
Why longitude determines time and latitude does not
How to read and interpret global coordinates in (lat, long) format
Why real time zones don't perfectly match longitude boundaries (political/economic reasons)
✅ Can Do
Identify the hemisphere and approximate location of a place from its coordinates
Calculate the time difference between two locations from their longitudes
Find local time at a given longitude given the time at another location
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Key Terms
LatitudeAngular distance north (N) or south (S) of the equator; ranges from 0° (equator) to 90°N (North Pole) or 90°S (South Pole)
LongitudeAngular distance east (E) or west (W) of the Prime Meridian (Greenwich); ranges from 0° to 180°E or 180°W
Prime MeridianThe 0° longitude line passing through Greenwich, England; the reference for both longitude and UTC time
International Date LineApproximately 180° longitude; crossing it going east subtracts a day; going west adds a day
Global coordinatesA pair (latitude°N/S, longitude°E/W) that uniquely identifies any point on Earth's surface
Misconceptions to Fix
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Wrong: Converting units only requires multiplying by 10.
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Right: Metric conversions use powers of 10, but area conversions use powers of 100 and volume uses powers of 1000.
Reading and Interpreting Global Coordinates
Key Point
Always check your units before substituting into formulas. Converting to consistent units is a common source of errors in assessment tasks.
Key Terms
FormulaA rule showing the relationship between variables using symbols.
SubstitutionReplacing variables with their known values in an equation.
Unit ConversionChanging a measurement from one unit to another.
CapacityThe amount of liquid a container can hold, measured in litres or millilitres.
PerimeterThe total distance around the outside of a shape.
AreaThe amount of space inside a two-dimensional shape.
What the Numbers Mean
Coordinates are always given as (latitude, longitude). The first number tells you how far north or south of the equator the place is; the second tells you how far east or west of Greenwich.
Location
Coordinates
Interpretation
Sydney, Australia
33.9°S, 151.2°E
Southern hemisphere; east of Greenwich
London, England
51.5°N, 0.1°W
Northern hemisphere; almost exactly on the Prime Meridian
New York, USA
40.7°N, 74.0°W
Northern hemisphere; west of Greenwich
Singapore
1.3°N, 103.8°E
Just north of the equator; east of Greenwich
Cape Town, South Africa
33.9°S, 18.4°E
Southern hemisphere; east of Greenwich
Key insight: Notice that Sydney and Cape Town share nearly the same latitude (both ≈ 34°S) but have very different longitudes — so they have similar climates (similar distance from the equator) but very different local times.
Calculating Time from Longitude
The 15° Rule
The Earth rotates 360° in 24 hours. Dividing: $360 \div 24 = 15°$ per hour. This means every 15° of longitude difference equals exactly 1 hour of time difference.
East is ahead: places east of you are further into the "future" relative to the Sun
West is behind: places west of you are further in the "past"
Must do — always work through UTC or use the difference: When given two longitudes, find the difference in degrees, divide by 15 to get hours. Then determine which location is ahead (east) and which is behind (west).
Common error — confusing latitude with longitude: Latitude has no effect on local time. Only longitude determines the time offset. Two cities on the same latitude circle (e.g. Sydney and Cape Town, both ≈ 34°S) can have very different local times.
Worked Example 1Interpreting Coordinates
Problem
A location has coordinates (27.5°S, 153.0°E). Describe its position and identify the approximate country.
Solution
1Latitude 27.5°S: approximately 28° south of the equator — Southern hemisphere, subtropicalS suffix means south of equator
2Longitude 153.0°E: approximately 153° east of the Prime MeridianE suffix means east of Greenwich
3Southern hemisphere + eastern Australia longitude → Brisbane, Queensland, Australia153°E is eastern Australia; 27.5°S places it in Queensland (south-east QLD)
Worked Example 2Time Difference from Longitude
Problem
City A is at longitude 120°E and City B is at longitude 75°W. It is 2:00 pm at City A.
(a) Find the longitude difference between the two cities.
(b) Calculate the time difference in hours.
(c) Find the local time at City B.
Solution
1(a) Longitude difference $= 120° + 75° = 195°$One city is east, the other is west of the Prime Meridian — add the two longitudes to find total separation
2(b) Time difference $= 195 \div 15 = \mathbf{13 \text{ hours}}$Divide longitude difference by 15
3City A is east (120°E), City B is west (75°W) → City A is ahead; City B is 13 h behindEast = ahead; west = behind
4(c) City B time $= 1400 - 13 = \mathbf{0100}$ (1:00 am — same day)City B is 13 hours behind City A; $14 - 13 = 1$ hour past midnight
Worked Example 3Time from Longitude — Via UTC
Problem
A location is at longitude 105°E. It is noon (1200) at the Prime Meridian (0°). What is the local time at 105°E?
Solution
1Time difference $= 105 \div 15 = 7 \text{ hours}$$105°$ of longitude ÷ 15° per hour = 7 hours
2105°E is east of the Prime Meridian → 7 hours aheadEast = ahead of UTC/Prime Meridian time
3Local time $= 1200 + 7 = \mathbf{1900}$ (7:00 pm)Add 7 hours to the Prime Meridian time
Practice
Practice Questions
Section A — Reading Coordinates
Describe the location of each place and identify its hemisphere:
(a) (35.7°N, 139.7°E) (b) (23.1°S, 43.2°W) (c) (1.3°N, 103.8°E)
Two cities both have latitude 40°N. One is at longitude 74°W (New York), the other at 116°E (Beijing). Explain why they have very different climates despite being on the same latitude.
Section B — Time from Longitude
Find the time difference (in hours) between longitudes: (a) 60°E and 0° (b) 135°E and 90°W (c) 45°W and 30°E
It is 6:00 am at the Prime Meridian. Find the local time at: (a) 60°E (b) 90°W (c) 150°E
A city is at longitude 120°E. It is 8:00 pm there. What is the time at the Prime Meridian?
City P is at 45°E and City Q is at 75°W. It is 10:00 am at City P. What is the local time at City Q?
Section C — Mixed Problems
Sydney is at approximately 151°E and Los Angeles is at approximately 118°W. Using only longitude, calculate the approximate time difference. If it is 10:00 am in Sydney, estimate the time in Los Angeles.
A ship crosses the International Date Line (180°) traveling eastward (from 179°E to 179°W). Does the ship move forward or backward one day in its calendar?
Q1
(a) 35.7°N, 139.7°E — Northern hemisphere, east of Greenwich: Tokyo, Japan; (b) 23.1°S, 43.2°W — Southern hemisphere, west of Greenwich: Rio de Janeiro, Brazil; (c) 1.3°N, 103.8°E — just north of equator, east: Singapore
Q2
Latitude affects climate (distance from equator → temperature). However, longitude has no effect on climate — it only affects local time. NY and Beijing are at similar distances from the equator but have different climates due to ocean currents, continental position, and other geographic factors. (Note: this is a conceptual question — the key point is latitude ≠ longitude.)
(a) 60°E, east → +4h: $0600+4=\mathbf{1000}$; (b) 90°W, west → −6h: $0600-6=\mathbf{0000}$ (midnight); (c) 150°E → +10h: $0600+10=\mathbf{1600}$
Q5
120°E → 8 h ahead; Prime Meridian = $2000-8=\mathbf{1200}$ (noon)
Q6
$\Delta\lambda = 45+75=120°$; time diff $=120÷15=8$ h; City P (45°E) is east → ahead; City Q (75°W) is 8 h behind P; City Q time $= 1000-8=\mathbf{0200}$ (2:00 am)
Q7
$\Delta\lambda = 151+118=269°$; time diff $=269÷15\approx 17.9$ h ≈ 18 h; Sydney (151°E) is ahead; LA (118°W) is 18 h behind; $1000-18=-0800$ → add 24 h → $\mathbf{1600}$ previous day (4:00 pm yesterday). Note: actual time zone difference is ~19 h including DST — this longitude estimate is approximate.
Q8
Crossing the Date Line eastward (from 179°E to 179°W) means moving from east to west in terms of longitudinal position — going from "ahead" time into "behind" time. The ship subtracts a day (goes back one calendar day). Eastward crossing = lose a day.
Revisit Your Initial Thinking
Look back at what you wrote in the Think First section. What has changed? What did you get right? What surprised you?
Multiple Choice
1 A city is at longitude 135°E. Based only on this longitude, its theoretical UTC offset is:
A UTC−9
B UTC+9
C UTC+135
D UTC+8
? Regarding this topic, 1 A city is at longitude 135°E. Based only on this longitude, its theoretical UTC offset is:
A UTC−9
B UTC+9
C UTC+135
D UTC+8
B - Correct!
B — $135 \div 15 = 9$; 135°E is east, so UTC+9. (Japan and Korea are at this longitude and do use UTC+9.) Option C confuses degrees with hours; Option A uses the correct magnitude but wrong sign.
2 City X is at 60°E and City Y is at 30°W. It is noon at City X. What is the local time at City Y?
A 6:00 am
B 8:00 am
C 2:00 pm
D 6:00 pm
? 2 City X is at 60°E and City Y is at 30°W. It is noon at City X. Identify the local time at City Y?
A 6:00 am
B 8:00 am
C 2:00 pm
D 6:00 pm
A - Correct!
A — $\Delta\lambda = 60 + 30 = 90°$; time diff $= 90 \div 15 = 6$ h; City X (60°E) is ahead → City Y (30°W) is 6 h behind; $1200 - 6 = 0600$ = 6:00 am.
3 Which statement about latitude is correct?
A Latitude determines local time
B The equator has latitude 180°
C Higher latitude values mean the location is further from the equator
D Sydney and London are at the same latitude
? Regarding this topic, 3 Which statement about latitude is correct?
A Latitude determines local time
B The equator has latitude 180°
C Higher latitude values mean the location is further from the equator
D Sydney and London are at the same latitude
C - Correct!
C — A larger absolute latitude value (e.g. 60° vs 30°) means further from the equator. Option A is wrong: longitude determines time, not latitude. Option B is wrong: the equator = 0°. Option D is wrong: Sydney ≈ 34°S, London ≈ 52°N.
Short Answer
01
SA 43 marks
A location has coordinates (22.3°S, 114.2°E).
(a) In which hemisphere is this location? (1 mark)
(b) Using the 15° rule, calculate the theoretical UTC offset for this longitude. (1 mark)
(c) If it is 0800 UTC, what is the local time at this location? (1 mark)
Work in your book
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(a)
22.3°S → Southern hemisphere
(b)
$114.2 \div 15 \approx 7.6$ h → theoretical UTC+7:36 (approximately UTC+7.5 or +8); accept UTC+7.6 or note this is close to UTC+8 (AWST)
Ship A (90°E) is east → ahead; Ship B (45°W) is 9 h behind; Ship B time = $1500 - 9 = \mathbf{0600}$ (6:00 am)
03
SA 65 marks
Sydney (33.9°S, 151.2°E) and Santiago, Chile (33.5°S, 70.7°W) are often called "sister cities" because they share nearly the same latitude.
(a) Explain why Sydney and Santiago have similar climates despite being on opposite sides of the world. (1 mark)
(b) Find the total difference in longitude between Sydney and Santiago. (1 mark)
(c) Calculate the time difference using the 15° rule. (1 mark)
(d) If it is 9:00 am in Sydney (AEST = UTC+10), find the local time in Santiago (using longitude only, not official time zone offsets). (2 marks)
Work in your book
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(a)
Both cities are approximately 34° from the equator (same latitude), so they receive similar amounts of solar energy annually, producing similar temperature ranges and seasonal patterns (Mediterranean-type climate).
Sydney (151.2°E) is east → ahead; Santiago (70.7°W) is 14.8 h behind Sydney; Sydney 0900 → Santiago $= 0900 - 14.8 \text{ h} = 0900 - 14\text{h}48\text{min}$; count back: $0900 - 14\text{h} = 1900$ prev day; $1900 - 48\text{min} = \mathbf{1812}$ previous day (6:12 pm the previous evening)