Longitude and Time Worksheet (a) What is longitude? (2 marks) 120W ... - Free Printable

Problem Analysis

The worksheet focuses on understanding the relationship between longitude and time, specifically how time changes as we move across different longitudes. The key concepts involved are:
1. Time Zones: Each 15° of longitude corresponds to a 1-hour difference in time.
2. Greenwich Mean Time (GMT): This is the reference point at 0° longitude.
3. Direction of Movement: Moving eastward from Greenwich increases the time, while moving westward decreases it.

We will solve each problem step by step, showing all working.

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Question 1

#### (a) What time will it be at 120°W if it is 11 am on Tuesday at 0° longitude?

- Step 1: Determine the time difference.
- Longitude difference = \( |120°W - 0°| = 120° \).
- Since each 15° corresponds to 1 hour, the time difference = \( \frac{120°}{15°/\text{hour}} = 8 \) hours.
- Moving westward (from 0° to 120°W) means the time is earlier.

- Step 2: Calculate the time at 120°W.
- If it is 11 am at 0°, subtract 8 hours: \( 11 \text{ am} - 8 \text{ hours} = 3 \text{ am} \).

- Answer: The time at 120°W is 3 am on Tuesday.

#### (b) If it is 6 am on Saturday at Greenwich (0°), what time will it be at 60°E?

- Step 1: Determine the time difference.
- Longitude difference = \( |60°E - 0°| = 60° \).
- Time difference = \( \frac{60°}{15°/\text{hour}} = 4 \) hours.
- Moving eastward (from 0° to 60°E) means the time is later.

- Step 2: Calculate the time at 60°E.
- If it is 6 am at 0°, add 4 hours: \( 6 \text{ am} + 4 \text{ hours} = 10 \text{ am} \).

- Answer: The time at 60°E is 10 am on Saturday.

#### (c) If it is 11:00 a.m. on Tuesday at 0° longitude, what time will it be at 105°E?

- Step 1: Determine the time difference.
- Longitude difference = \( |105°E - 0°| = 105° \).
- Time difference = \( \frac{105°}{15°/\text{hour}} = 7 \) hours.
- Moving eastward (from 0° to 105°E) means the time is later.

- Step 2: Calculate the time at 105°E.
- If it is 11:00 a.m. at 0°, add 7 hours: \( 11:00 \text{ a.m.} + 7 \text{ hours} = 6:00 \text{ p.m.} \).

- Answer: The time at 105°E is 6:00 p.m. on Tuesday.

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Question 2

#### (a) If it is 2 p.m. on Monday at 0° longitude, what time will it be at 97°E?

- Step 1: Determine the time difference.
- Longitude difference = \( |97°E - 0°| = 97° \).
- Time difference = \( \frac{97°}{15°/\text{hour}} = 6 \text{ hours and } \frac{7°}{15°/\text{hour}} = 6 \text{ hours and } 28 \text{ minutes} \).
- Moving eastward (from 0° to 97°E) means the time is later.

- Step 2: Calculate the time at 97°E.
- If it is 2 p.m. at 0°, add 6 hours and 28 minutes: \( 2:00 \text{ p.m.} + 6 \text{ hours and } 28 \text{ minutes} = 8:28 \text{ p.m.} \).

- Answer: The time at 97°E is 8:28 p.m. on Monday.

#### (b) If it is 4:00 p.m. on Friday at 0° longitude, what time will it be at 87°W?

- Step 1: Determine the time difference.
- Longitude difference = \( |87°W - 0°| = 87° \).
- Time difference = \( \frac{87°}{15°/\text{hour}} = 5 \text{ hours and } \frac{12°}{15°/\text{hour}} = 5 \text{ hours and } 48 \text{ minutes} \).
- Moving westward (from 0° to 87°W) means the time is earlier.

- Step 2: Calculate the time at 87°W.
- If it is 4:00 p.m. at 0°, subtract 5 hours and 48 minutes: \( 4:00 \text{ p.m.} - 5 \text{ hours and } 48 \text{ minutes} = 10:12 \text{ a.m. on Friday} \).

- Answer: The time at 87°W is 10:12 a.m. on Friday.

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Question 3

#### (a) Calculate the time at 120°W if it is 4 p.m. on Sunday at a place located at 40°E.

- Step 1: Determine the time difference between 40°E and 120°W.
- Longitude difference = \( |120°W - 40°E| = 120° + 40° = 160° \).
- Time difference = \( \frac{160°}{15°/\text{hour}} = 10 \text{ hours and } \frac{10°}{15°/\text{hour}} = 10 \text{ hours and } 40 \text{ minutes} \).
- Moving from 40°E to 120°W means the time is earlier.

- Step 2: Calculate the time at 120°W.
- If it is 4 p.m. at 40°E, subtract 10 hours and 40 minutes: \( 4:00 \text{ p.m.} - 10 \text{ hours and } 40 \text{ minutes} = 5:20 \text{ a.m. on Sunday} \).

- Answer: The time at 120°W is 5:20 a.m. on Sunday.

#### (b) Calculate the time at 75°W if it is 4:00 p.m. on Sunday at a place located at 75°W.

- Step 1: Determine the time difference between 75°W and 75°W.
- Longitude difference = \( |75°W - 75°W| = 0° \).
- Time difference = 0 hours.

- Step 2: Calculate the time at 75°W.
- If it is 4:00 p.m. at 75°W, the time remains the same.

- Answer: The time at 75°W is 4:00 p.m. on Sunday.

#### (c) Calculate the time at 105°E if it is 3 p.m. on Thursday at a place located at 45°W.

- Step 1: Determine the time difference between 45°W and 105°E.
- Longitude difference = \( |105°E - 45°W| = 105° + 45° = 150° \).
- Time difference = \( \frac{150°}{15°/\text{hour}} = 10 \) hours.
- Moving from 45°W to 105°E means the time is later.

- Step 2: Calculate the time at 105°E.
- If it is 3 p.m. at 45°W, add 10 hours: \( 3:00 \text{ p.m.} + 10 \text{ hours} = 1:00 \text{ a.m. on Friday} \).

- Answer: The time at 105°E is 1:00 a.m. on Friday.

#### (d) Calculate the time at 15°E if it is 5 a.m. on Friday at a place located at 135°E.

- Step 1: Determine the time difference between 135°E and 15°E.
- Longitude difference = \( |135°E - 15°E| = 120° \).
- Time difference = \( \frac{120°}{15°/\text{hour}} = 8 \) hours.
- Moving from 135°E to 15°E means the time is earlier.

- Step 2: Calculate the time at 15°E.
- If it is 5 a.m. at 135°E, subtract 8 hours: \( 5:00 \text{ a.m.} - 8 \text{ hours} = 9:00 \text{ p.m. on Thursday} \).

- Answer: The time at 15°E is 9:00 p.m. on Thursday.

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Question 4

#### (a) Find the longitude of a given place if it is 1 p.m. on Thursday at Greenwich (0°) and the time at the other places is 5 p.m.

- Step 1: Determine the time difference.
- Time difference = \( 5 \text{ p.m.} - 1 \text{ p.m.} = 4 \) hours.
- Since the time is later, the place is east of Greenwich.

- Step 2: Calculate the longitude.
- Longitude difference = \( 4 \text{ hours} \times 15°/\text{hour} = 60° \).
- The place is at \( 60°E \).

- Answer: The longitude is 60°E.

#### (b) Find the longitude of a given place if it is 4 a.m. on Tuesday at Greenwich (0°) and the time at the other places is 7 a.m.

- Step 1: Determine the time difference.
- Time difference = \( 7 \text{ a.m.} - 4 \text{ a.m.} = 3 \) hours.
- Since the time is later, the place is east of Greenwich.

- Step 2: Calculate the longitude.
- Longitude difference = \( 3 \text{ hours} \times 15°/\text{hour} = 45° \).
- The place is at \( 45°E \).

- Answer: The longitude is 45°E.

#### (c) Find the longitude of a given place if it is 3 p.m. on Wednesday at Greenwich (0°) and the time at the other places is 11 p.m.

- Step 1: Determine the time difference.
- Time difference = \( 11 \text{ p.m.} - 3 \text{ p.m.} = 8 \) hours.
- Since the time is later, the place is east of Greenwich.

- Step 2: Calculate the longitude.
- Longitude difference = \( 8 \text{ hours} \times 15°/\text{hour} = 120° \).
- The place is at \( 120°E \).

- Answer: The longitude is 120°E.

#### (d) Find the longitude of the given places if it is 10 a.m. Saturday at 45°W and the time at the other places is 5 p.m.

- Step 1: Determine the time difference.
- Time difference = \( 5 \text{ p.m.} - 10 \text{ a.m.} = 7 \) hours.
- Since the time is later, the place is east of 45°W.

- Step 2: Calculate the longitude.
- Longitude difference = \( 7 \text{ hours} \times 15°/\text{hour} = 105° \).
- The place is \( 45°W + 105° = 60°E \).

- Answer: The longitude is 60°E.

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Final Answers

1. (a) 3 am on Tuesday
(b) 10 am on Saturday
(c) 6:00 p.m. on Tuesday

2. (a) 8:28 p.m. on Monday
(b) 10:12 a.m. on Friday

3. (a) 5:20 a.m. on Sunday
(b) 4:00 p.m. on Sunday
(c) 1:00 a.m. on Friday
(d) 9:00 p.m. on Thursday

4. (a) 60°E
(b) 45°E
(c) 120°E
(d) 60°E

\boxed{60^\circ E}