Mathematics Standard • Year 11 • Module 2 • Lesson 22
Latitude, Longitude, and Location — Skill Drill
Drill the 15°-per-hour rule: convert between longitude differences and time differences, and find local time at any longitude from a Prime Meridian reference.
1. Quick recall
Answer each question in the space provided. 1 mark each
Q1.1 The Earth rotates ____° in 24 hours, so 1 hour of time = ____° of longitude, and 1° of longitude = ____ minutes of time.
Q1.2 Coordinates are written as ____________, ____________. The first value ranges from 0° (____________) to 90° N/S (the poles). The second ranges from 0° (the ____________ Meridian, through Greenwich) to 180° E/W.
Q1.3 Places EAST of you are ____________ in time; places WEST are ____________ in time. Latitude does / does not affect local time (circle one).
2. Worked example — local time from longitude
Every line of working has a reason on the right.
Problem. A city is at longitude 75°E. It is 12:00 noon at the Prime Meridian (0°). Find the local time at this city.
Step 1 — Time difference in hours.
Δt = Δλ ÷ 15 = 75 ÷ 15 = 5 h
Reason: each 15° of longitude = 1 hour of time.
Step 2 — Determine direction.
75°E is east of 0° → 5 hours ahead of the Prime Meridian.
Reason: east = ahead (sun rises in the east first).
Step 3 — Add the offset to the reference time.
Local time = 1200 + 5 h = 1700
Reason: Prime Meridian time + offset = local time.
Conclusion. Local time at 75°E = 1700 (5:00 pm).
3. Faded example — fill in the missing steps
City P is at longitude 30°E and City Q is at longitude 105°W. It is 4:00 pm at City P. Find the local time at City Q. 4 marks
Step 1 — Δλ: one east, one west → Δλ = ____ + ____ = ____°
Step 2 — Δt: Δt = ____ ÷ 15 = ____ h
Step 3 — Direction: City P (____) is ____________ of City Q → City Q is ____ hours BEHIND.
Step 4 — Subtract: Q time = 1600 − ____ = ____________ → if negative, add 2400 = ____________
Conclusion. Q time = ____________ (state day if relevant).
4. Graduated practice — longitude and time
Show your working. State time as 24-hour and identify the day if it changes.
Foundation — single-step recall (4 questions)
| Q | Problem | Answer |
|---|---|---|
| 4.1 1 | How many hours' time difference equates to 90° of longitude? | |
| 4.2 1 | How many minutes of time = 7° of longitude? | |
| 4.3 1 | State the theoretical UTC offset for a city at longitude 60°E. | |
| 4.4 1 | State the hemisphere(s) of the location (50°S, 100°W). |
Standard — typical HSC difficulty (6 questions)
Always determine direction (E ahead / W behind) before adjusting the time.
4.5 It is 0800 at the Prime Meridian. Find the local time at longitude 45°E. 2 marks
4.6 It is 1400 at the Prime Meridian. Find the local time at longitude 120°W. 2 marks
4.7 A city at longitude 135°E shows 8:00 pm local. Find the time at the Prime Meridian. 2 marks
4.8 City A is at 60°E, City B is at 30°W. It is 1100 at City A. Find the time at City B. 2 marks
4.9 Sydney (≈ 150°E) and London (≈ 0°). It is 6:00 am Wednesday in London. Use the 15°-rule (not the official AEDT offset) to find the time in Sydney. 2 marks
4.10 What is the latitude of the equator? What is the longitude of the Prime Meridian? 2 marks
Extension — fractional longitudes / date line (2 questions)
4.11 A location is at longitude 142.5°E. (a) Calculate its theoretical UTC offset, in hours and minutes. (b) If it is 1500 UTC, find the local time at this location. 3 marks
4.12 A ship sails eastward across the International Date Line (180°), from 179°E to 179°W. (a) State, in words, what happens to the ship's calendar day. (b) Explain in one sentence why this is necessary. 3 marks
5. Self-check the easy 3
Tick once you've verified each method.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1 — 15° rule recall
Earth rotates 360° in 24 h. 1 hour = 15°; 1° = 4 minutes.
Q1.2 — Coordinate format
(latitude°N/S, longitude°E/W). Latitude 0° = equator; longitude 0° = Prime Meridian.
Q1.3 — East vs west, latitude irrelevance
East = ahead. West = behind. Latitude does NOT affect local time.
Q3 — Faded example (30°E vs 105°W, P 4 pm)
Step 1: Δλ = 30 + 105 = 135°. Step 2: Δt = 135 ÷ 15 = 9 h. Step 3: P (30°E) is east of Q → Q is 9 h behind. Step 4: Q = 1600 − 9 = 0700 (no negative, no rollover). Conclusion: Q time = 0700 (7:00 am) same day.
Q4.1 — 90° in hours
90 ÷ 15 = 6 h.
Q4.2 — 7° in minutes
7 × 4 = 28 min.
Q4.3 — 60°E offset
60 ÷ 15 = 4; east → UTC+4.
Q4.4 — Hemisphere of (50°S, 100°W)
Southern hemisphere (because of S) and western half (because of W).
Q4.5 — 0800 at PM → 45°E
Δt = 45 ÷ 15 = 3 h; east → ahead → 0800 + 3 = 1100.
Q4.6 — 1400 at PM → 120°W
Δt = 120 ÷ 15 = 8 h; west → behind → 1400 − 8 = 0600 same day.
Q4.7 — 135°E shows 2000 → PM time
Δt = 135 ÷ 15 = 9 h; 135°E is 9 h ahead → PM = 2000 − 9 = 1100.
Q4.8 — A 60°E (1100) → B 30°W
Δλ = 60 + 30 = 90°; Δt = 90 ÷ 15 = 6 h. A is east of B → B is 6 h behind → B = 1100 − 6 = 0500 (5:00 am).
Q4.9 — Sydney (150°E) from London 6 am Wed
Δt = 150 ÷ 15 = 10 h ahead. Sydney = 0600 + 10 = 1600 Wednesday (4:00 pm Wed).
Q4.10 — Equator and Prime Meridian
Equator latitude = 0°. Prime Meridian longitude = 0°.
Q4.11 — 142.5°E offset and local time
(a) 142.5 ÷ 15 = 9.5 → UTC+9:30.
(b) 1500 UTC + 9:30 = 2430 → subtract 2400 → 0030 next day.
Q4.12 — Crossing the Date Line eastward
(a) The ship moves back one calendar day (e.g. from Monday to Sunday) when it crosses 180° heading east. (b) Without this adjustment, travelling fully around the world east would gain a day relative to a stationary observer, so the Date Line keeps everyone's calendars in sync.