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Ignition Learning — Activity Sheet

Duration, time zones & real-world rates

Mathematics · Year 8

Name: ______________________Date: ____________

Working with duration means finding the time between a start and end point, often across 12-hour (am/pm) or 24-hour time, and sometimes across different time zones. Australia alone spans three time zones (Eastern, Central, Western), and international travel or online meetings often require converting between them. Rates compare two related quantities measured in different units — speed (km/h), pay ($/hour), or fuel consumption (L/100km) are all rates. Solving real rate problems, like working out travel time from distance and speed, or the cheaper of two shopping options, is one of the most practical everyday applications of maths.

Example

A flight leaves Perth (Western Australia) at 9:00am and takes 4 hours to reach Sydney (Eastern Australia, 2 hours ahead when Perth doesn't observe daylight saving). Departure in Sydney time is 11:00am; adding the 4-hour flight gives an arrival of 3:00pm Sydney time — even though only 4 hours actually passed in the air.

Key terms

Duration:: The length of time between a start and end point.
Rate:: A comparison of two related quantities measured in different units, like km/h.

Questions

1. Duration means:
- The length of time between a start and end point
- Only the starting time
- Only the ending time
- A type of angle
2. A rate compares two related quantities measured in:
- Different units
- Identical units always
- No units at all
- Only money
3. Speed measured in km/h is an example of a:
- Rate
- Duration
- An angle
- A shape
4. Australia spans how many time zones?
- Three
- One
- Five
- Ten
5. 24-hour time avoids confusion between:
- am and pm
- Days of the week
- Months of the year
- Different countries only
6. Pay measured in $/hour is an example of a:
- Rate
- Duration
- A fraction only
- An angle
7. Converting between time zones is often needed for:
- International travel or online meetings
- Measuring area only
- Solving triangles only
- Nothing practical
8. A car travels 240km in 3 hours. Its speed (rate) is:
- 80km/h
- 720km/h
- 243km/h
- 80km
9. A flight takes off at 14:20 and lands at 17:05. Its duration is:
- 2h 45min
- 2h 15min
- 3h 15min
- 2h 20min
10. If Sydney is 2 hours ahead of Perth, and it is 10:00am in Perth, the time in Sydney is:
- 12:00pm
- 8:00am
- 10:00am
- 2:00pm
11. A worker earns $28/hour and works 6 hours. Total pay is:
- $168
- $34
- $22
- $188
12. Converting 3:00pm to 24-hour time gives:
- 15:00
- 03:00
- 13:00
- 17:00
13. A car uses 6L of fuel per 100km. How much fuel for a 250km trip?
- 15L
- 6L
- 25L
- 1500L
14. A meeting starts at 09:00 Sydney time. If Perth is 2 hours behind, what time is it in Perth?
- 07:00
- 11:00
- 09:00
- 10:00
15. Two phone plans: Plan A charges $0.10/min, Plan B charges a flat $15 for unlimited calls. At what number of minutes do they cost the same?
- 150 minutes
- 15 minutes
- 1.5 minutes
- 1500 minutes
16. A flight leaves Perth at 9:00am and takes 4 hours to reach Sydney, which is 2 hours ahead. What is the arrival time in Sydney time?
- 3:00pm
- 1:00pm
- 11:00am
- 5:00pm
17. A recipe requires ingredients in the ratio of a rate: 2 eggs per 100g of flour. How many eggs for 350g of flour?
- 7 eggs
- 3.5 eggs
- 5 eggs
- 2 eggs
18. Why is understanding time zone differences important when scheduling an online meeting between Perth and Sydney?
- A meeting time announced in one city's local time will be a different clock time in the other, risking a missed meeting
- Time zones have no real effect on scheduling
- All Australian cities share an identical local time year-round
- Online meetings automatically adjust without any need for calculation
19. Comparing 500g for $4 versus 750g for $5.50, which is the better value per 100g?
- The 750g option is cheaper per 100g (≈$0.73 vs $0.80)
- The 500g option is always cheaper
- Both options cost exactly the same per 100g
- This cannot be compared without more information
20. A logistics company schedules deliveries between Perth and Sydney warehouses. Why would ignoring the 2-hour time zone difference risk real operational problems?
- Scheduled pickup or delivery times could be misread by 2 hours, causing missed deliveries or idle staff
- Time zone differences have no effect on delivery scheduling
- Perth and Sydney always share an identical local time
- Logistics companies never need to account for time zones
21. Understanding duration, time zones and rates mainly helps you to:
- Solve practical, everyday problems involving time and comparing quantities fairly
- Avoid ever comparing two different measurements
- Assume all rates and durations are irrelevant to real life
- Ignore time zone differences when travelling or scheduling

Answer key (parent copy)

1. The length of time between a start and end point
2. Different units
3. Rate
4. Three
5. am and pm
6. Rate
7. International travel or online meetings
8. 80km/h
9. 2h 45min
10. 12:00pm
11. $168
12. 15:00
13. 15L
14. 07:00
15. 150 minutes
16. 3:00pm
17. 7 eggs
18. A meeting time announced in one city's local time will be a different clock time in the other, risking a missed meeting
19. The 750g option is cheaper per 100g (≈$0.73 vs $0.80)
20. Scheduled pickup or delivery times could be misread by 2 hours, causing missed deliveries or idle staff
21. Solve practical, everyday problems involving time and comparing quantities fairly