Mathematics Standard • Year 11 • Module 2 • Lesson 22
Latitude, Longitude, and Location — Problem Set
Apply the 15°-per-hour rule and (lat, long) interpretation to real Australian and global locations — including sister-cities, ship crossings, and broadcast timing.
Problem 1 — Reading global coordinates
Three Australian and overseas cities have approximate coordinates:
Brisbane (27.5°S, 153.0°E)
Cape Town (33.9°S, 18.4°E)
Honolulu (21.3°N, 157.9°W)
Set up: What are we solving for?
(i) State the hemisphere(s) of each city. 1 mark
(ii) Calculate the theoretical UTC offset (to 1 d.p. of hours) of each city using only the longitude. 3 marks
(iii) Cape Town and Brisbane have nearly the same latitude. Explain in one sentence why they have similar climate but very different local times. 1 mark
Stuck? Latitude → climate; longitude → time.Problem 2 — Two cities, two hemispheres
Ship A is anchored at longitude 75°E (in the Indian Ocean). Ship B is anchored at longitude 60°W (in the Atlantic Ocean). It is 2:00 pm at Ship A.
Set up: What are we solving for?
(i) Calculate the longitude difference Δλ. 1 mark
(ii) Calculate the time difference Δt in hours. 1 mark
(iii) Determine which ship is ahead in time and find the local time at Ship B. 3 marks
Stuck on direction? 75°E is east of the Prime Meridian; 60°W is west. East = ahead, so Ship A is ahead and Ship B is behind.Problem 3 — Cities with half-hour offsets
India (Delhi) is at approximately 77.5°E, and its time zone (IST) is officially UTC+5:30.
Set up: What are we solving for?
(i) Use the 15°-per-hour rule to calculate the theoretical offset based on Delhi's longitude. Express the answer in hours and minutes. 2 marks
(ii) By how many minutes does the theoretical offset differ from the official IST offset of UTC+5:30? 1 mark
(iii) If it is 1200 UTC, calculate Delhi's local time using the official IST offset. 2 marks
Stuck on (i)? 77.5 ÷ 15 = 5.166… hours = 5 h plus (0.166… × 60) min = 5 h 10 min. The official IST rounds this to UTC+5:30 for political simplicity.Problem 4 — Sailing ship and the Date Line
A research vessel departs Fiji (179°E) on Wednesday and sails eastward, crossing the International Date Line at 180° / 180°. After crossing, it continues to a station at 175°W.
Set up: What are we solving for?
(i) State, in one sentence, what happens to the ship's calendar day at the moment it crosses the Date Line going eastward. 1 mark
(ii) What is the longitude difference between Fiji (179°E) and the station (175°W), measured the short way around? 2 marks
(iii) Find the local time difference between Fiji and the station, in hours and minutes. State which is ahead in time. 2 marks
Stuck on (ii)? The short way is across 180°: 1° from 179°E to 180°, then 5° from 180° to 175°W → total 6°.Problem 5 — Live event using longitude alone
A scientific conference is being livestreamed from a research base at exactly 45°W longitude (think: a station in eastern South America). The talk begins at 9:00 am local time, Monday.
Set up: What are we solving for?
(i) Using the 15°-per-hour rule, find the theoretical UTC offset of the base. 1 mark
(ii) Find the UTC time when the talk begins. 1 mark
(iii) A viewer in Sydney is at approximately 151°E longitude. Using only longitude (15°-rule), find the Sydney local time and day when the talk begins. 3 marks
Stuck? Sydney's longitude-based offset ≈ 151/15 ≈ 10.07 h. UTC time + 10.07 h gives Sydney time, rounded.How did this worksheet feel?
What I'll revisit before next class:
Problem 1 — Reading coordinates
Set up. Read N/S for hemisphere; use longitude ÷ 15 for UTC offset; reason about latitude vs longitude effects.
(i) Brisbane: Southern, Eastern. Cape Town: Southern, Eastern. Honolulu: Northern, Western.
(ii) Brisbane: 153 ÷ 15 = 10.2 → UTC+10.2 h (≈ UTC+10:12). Cape Town: 18.4 ÷ 15 ≈ 1.23 → UTC+1.2 h (≈ UTC+1:14). Honolulu: 157.9 ÷ 15 ≈ 10.53 → UTC−10.5 h (negative because west).
(iii) Climate is determined by distance from the equator (latitude); both cities are ≈ 28°–34°S, so both have similar mediterranean/subtropical climates. Local time is determined by longitude — Brisbane (153°E) and Cape Town (18°E) are 135° apart, so their local times differ by ≈ 9 hours.
Problem 2 — Ship A (75°E) and Ship B (60°W)
Set up. Add the two longitudes (different hemispheres) for Δλ, divide by 15 for Δt, decide direction.
(i) Δλ = 75 + 60 = 135°.
(ii) Δt = 135 ÷ 15 = 9 h.
(iii) Ship A (75°E) is east → ahead; Ship B (60°W) is 9 h behind. B = 1400 − 9 = 0500 (5:00 am) same day.
Problem 3 — Delhi 77.5°E and IST
Set up. Convert longitude to a theoretical offset, then compare to the official offset.
(i) 77.5 ÷ 15 = 5.166… = 5 h + 0.166… × 60 min = 5 h 10 min → UTC+5:10.
(ii) Official IST = UTC+5:30; difference = 5:30 − 5:10 = 20 minutes (Delhi's actual clock is 20 min ahead of its longitude-based time).
(iii) Delhi = 1200 UTC + 5:30 = 1730 (5:30 pm).
Problem 4 — Date Line eastward crossing
Set up. State the Date Line rule, compute the short longitude difference, divide by 15 for time, decide direction.
(i) Eastward crossing of 180° → ship's calendar moves back one day (e.g. Wednesday becomes Tuesday in the same instant).
(ii) Short way: 179°E → 180° = 1°; 180° → 175°W = 5°; total = 6°.
(iii) Δt = 6 × 4 = 24 min, or 6 ÷ 15 = 0.4 h = 0 h 24 min. Fiji is west of the station (after the crossing, the station is at higher longitude when measured eastward), but in geographical terms, going east still means later time. Actually: 175°W is east of 179°E (measured the short way). So the station is 24 min ahead of Fiji's clock (despite the Date Line, the local time at 175°W runs slightly ahead of the local time at 179°E because the station is 6° further east along the short arc).
Problem 5 — Conference at 45°W
Set up. Find UTC offset of base via 15°-rule, convert local → UTC, then UTC → Sydney via Sydney's longitude.
(i) 45 ÷ 15 = 3 h; west → UTC−3.
(ii) Local 0900 − (−3) = 0900 + 3 = 1200 UTC Monday.
(iii) Sydney longitude ≈ 151°E → offset ≈ 151 ÷ 15 ≈ 10.07 h east. Sydney local ≈ 1200 + 10.07 ≈ 2204 → ~10:04 pm Monday in Sydney. (Note: the official AEDT offset of +11 in summer would give 2300, but using only longitude gives ≈ 2204.)