How Far?
Calculate using the 24-hour clock and time zones
Devise and use problem solving strategies to explore situations mathematically (make a drawing, be systematic)
The key to this problem is the wording. When the plane lands ‘at Sydney airport at 2:30pm’ it means 2:30pm Sydney time.
In order to be able to do this problem, students need to know about the Earth’s time zones.
In discussion, students may think that, although Sydney is further away than Christchurch, the plane travelling to Sydney flies much faster than the one to Christchurch. But the two planes are the same and probably fly at very similar speeds. You might get them to check how fast the plane to Sydney would have to fly to get there at the same time as the other plane reached Christchurch.
Note that in this problem the actual times are approximate. It would be a good exercise for the students to find out the actual times of flights between Auckland and Christchurch and Auckland and Sydney from www.airnewzealand.co.nz. or other airline website.
Problem
At 1:00pm, two aircraft take off, one after the other, from Auckland airport. One lands at Christchurch airport at 2:30pm and the other lands at Sydney airport at 2:30pm. Does that mean that Christchurch and Sydney are both the same distance from Auckland?
If not, how long does the plane going to Sydney actually take?
Teaching Sequence
- Pose the problem to the class. Allow time to think before asking for ideas from the class.
- Ask: Are they the same distance from Auckland? Most students will know that Christchurch is closer but if not a quick look at a globe or map of the world should confirm this.
- Ask: How is it possible for the planes to arrive at the same time? There are many ways for students to have prior knowledge of time zones eg international travel, live TV coverage of international events.
- Discuss the use of time zone information.
- Repose the problem for the students to work on.
-
Share solutions.
Solution to the problem
By looking at a globe students should quickly be able to see that Sydney is further away from Auckland than Christchurch is. Why are the two planes able to land at the same time?
Sydney and Auckland are in two different time zones. When it is 1:00pm in Auckland it is 11:00am in Sydney. Hence when the plane lands in Sydney at 2:30pm, it is 4:30pm in Auckland. Hence the plane has actually taken three and a half hours to get to Sydney. (The plane going to Christchurch landed there two hours before this.)
| Attachment | Size |
|---|---|
| HowFar.pdf | 36.59 KB |
| HowFarMaori.pdf | 51.05 KB |
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