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Module 2 · L22 of 22 ~55–60 min MS-M3 · NEW 2024 ⚡ +95 XP available

Latitude, Longitude, and Location

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.

Today's hook, The Earth takes 24 hours to rotate 360°. Sydney is at roughly 151°E longitude. If noon occurs at 0° longitude right now, how long until noon reaches Sydney? This question is the reason Sydney uses UTC+10.

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Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

Worksheets

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Three printable worksheets that build from foundations to mastery, or build your own from any module’s questions.

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Recall, your gut answer first

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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.

Without calculating 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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The formulas you need to own

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Latitude and longitude calculations rest on two key relationships. Lock these in, both appear in HSC exam questions.

Latitude measures angular distance north or south of the equator (0° to 90°N or 90°S). Longitude measures angular distance east or west of the Prime Meridian (0° to 180°E or 180°W). Longitude determines local time, latitude does not.

Latitude and longitude form a grid that locates any point on Earth and links longitude to time.

UTC offsets and key cities from UTC−8 to UTC+12.

$\Delta t \text{ (hours)} = \dfrac{\Delta\lambda\text{ (degrees)}}{15}$

East = ahead

East longitude is ahead of UTC (+). 120°E → UTC+8. 150°E → UTC+10. The Sun reaches eastern longitudes first.

West = behind

West longitude is behind UTC (−). 60°W → UTC−4. 75°W → UTC−5. Western cities are earlier in the day.

One and four

15° = 1 hour. 1° = 4 minutes. Easy to remember: 360° ÷ 24 h = 15°/h; 60 min ÷ 15° = 4 min/°.

What you'll master

Know

Key facts

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

Concepts

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

Skills

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

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.

15° ruleThe Earth rotates 15° of longitude per hour, so every 15° of longitude difference between two places equals a 1-hour time difference.

Reading and interpreting global coordinates

Coordinates are always given as (latitude, longitude).

Reading and interpreting global coordinates

core concept

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.

Global coordinates: (latitude°N/S, longitude°E/W). Latitude: 0° at equator, 90° at poles. Longitude: 0° at Prime Meridian (Greenwich), up to 180° E or W. Same latitude = same distance from equator. Same longitude = same meridian.

Pause, copy the latitude definition (degrees north or south of the equator; range 0°–90° N/S), the longitude definition (degrees east or west of the Prime Meridian; range 0°–180° E/W), and the key reference lines (equator = 0° latitude; Prime Meridian through Greenwich = 0° longitude) into your book.

Did you get this? True or false: latitude determines local time, while longitude determines climate and distance from the equator.

Worked examples · 3 in a row, reveal as you go

PROBLEM 1 · INTERPRETING COORDINATES

A location has coordinates (27.5°S, 153.0°E). Describe its position and identify the approximate country.

Latitude 27.5°S: approximately 28° south of the equator, Southern hemisphere, subtropical

S suffix means south of equator.

PROBLEM 2 · TIME DIFFERENCE FROM LONGITUDE

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. (b) Calculate the time difference. (c) Find the local time at City B.

(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.

PROBLEM 3 · TIME FROM LONGITUDE, VIA UTC

A location is at longitude 105°E. It is noon (1200) at the Prime Meridian (0°). What is the local time at 105°E?

Time difference $= 105 \div 15 = 7 \text{ hours}$

$105°$ of longitude ÷ 15° per hour = 7 hours.

Quick check: A city is at longitude 135°E. Based only on this longitude, its theoretical UTC offset is:

Common errors · the 3 traps that cost marks

Trap 01

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 because they are at different longitudes (151°E vs 18°E).

Trap 02

Adding longitudes when you should subtract (or vice versa)

Both cities east of Greenwich → subtract to get difference (e.g. 120°E and 60°E → difference = 60°). One east, one west → add the values (e.g. 120°E and 75°W → difference = 195°). Mixing these up is the most common error in longitude questions.

Trap 03

Using latitude to calculate time difference

If you're given two coordinates (lat, long) and asked for a time difference, only the longitude values matter. You can completely ignore the latitude values for time calculations. The formula $\Delta t = \Delta\lambda \div 15$ uses longitude only.

Fill the gap: The Earth rotates ° in 24 hours, which means it rotates ° per hour. Therefore every 1° of longitude equals minutes of time difference.

Quick-fire practice · 8 calculations

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.

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?

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?

Odd one out: Three of these statements are correct about longitude and time. Which one is wrong?

Revisit your thinking

Earlier you were asked: if noon occurs at 0° longitude right now, how long until noon reaches Sydney (151°E)?

Revisit your thinking

Earlier you were asked: if noon occurs at 0° longitude right now, how long until noon reaches Sydney (151°E)?

Earth rotates 15° per hour.
Time for Sun to travel 151°: $151 \div 15 \approx 10.07$ hours ≈ 10 hours 4 minutes.
This is why Sydney's standard time offset is UTC+10, longitude 150°E (the nearest standard meridian) gives exactly $150 \div 15 = 10$ hours.
The slight discrepancy (151° instead of 150°) is why AEST is "approximately" UTC+10 rather than a perfect fit, politics and practicality round time zones to whole (or half) hours.

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Show what you have learned

Multiple choice, then short answer under exam conditions.

Multiple choice

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Short answer

ApplyBand 43 marks

Q1. 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)

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ApplyBand 44 marks

Q2. Two ships communicate by radio. Ship A is at longitude 90°E and Ship B is at longitude 45°W. It is 3:00 pm at Ship A.

(a) Find the difference in longitude between the two ships. (1 mark)

(b) Find the time difference in hours and minutes. (1 mark)

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AnalyseBand 55 marks

Q3. 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)

(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)

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📖 Comprehensive answers (click to reveal)

Drill answers: 1(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 · 2: Latitude affects climate (distance from equator → temperature) but longitude has no effect on climate, NY and Beijing are at similar distances from the equator but climate differs due to ocean currents and continental position. · 3(a) $60÷15=\mathbf{4\text{ h}}$; (b) $135+90=225°$; $225÷15=\mathbf{15\text{ h}}$; (c) $45+30=75°$; $75÷15=\mathbf{5\text{ h}}$ · 4(a) 60°E → +4h: $0600+4=\mathbf{1000}$; (b) 90°W → −6h: $0600-6=\mathbf{0000}$ (midnight); (c) 150°E → +10h: $0600+10=\mathbf{1600}$ · 5: 120°E → 8 h ahead; PM = $2000-8=\mathbf{1200}$ (noon) · 6: $\Delta\lambda=45+75=120°$; $\Delta t=8$ h; City Q = $1000-8=\mathbf{0200}$ · 7: $\Delta\lambda=151+118=269°$; $\Delta t\approx18$ h; LA = $1000-18=\mathbf{1600}$ previous day · 8: Crossing eastward (179°E→179°W) → subtract a day (go back one calendar day)

Q1 (3 marks): (a) 22.3°S → Southern hemisphere [1] (b) $114.2 \div 15 \approx 7.6$ h → theoretical UTC+7.6 (≈ UTC+8) [1] (c) $0800 + 7\text{h}36\text{min} = \mathbf{1536}$ (3:36 pm) [1]

Q2 (4 marks): (a) $90 + 45 = \mathbf{135°}$ [1] (b) $135 \div 15 = \mathbf{9 \text{ hours}}$ [1] (c) Ship A (90°E) is east → ahead; Ship B time = $1500 - 9 = \mathbf{0600}$ (6:00 am) [2]

Q3 (5 marks): (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). [1] (b) $151.2 + 70.7 = \mathbf{221.9°}$ [1] (c) $221.9 \div 15 \approx \mathbf{14.8 \text{ h}}$ (approximately 14 h 47 min) [1] (d) Sydney (151.2°E) is east → ahead; Santiago (70.7°W) is 14.8 h behind; $0900 - 14\text{h}48\text{min} = \mathbf{1812}$ previous day (6:12 pm the previous evening) [2]

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Five timed questions on latitude, longitude, and time calculations. Beat the boss to bank a tier, gold (90% + speed), silver (75%), or bronze (50%). Replays welcome.

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Module 2 overview · Year 11 Maths Standard