2.4+Walking+to+Win+10-11

**Z.H**
 * 5/13/11**
 * __Big Idea__: Many real world situations can be modelled and predicted using mathematics**
 * __Essential Question__: What is the relationship between a table, graph, and an equation?**


 * __Notes__-** We talked about how graphs can be used to show differences between 2 lines. We also had time to discuss with our table groups what we thought helped show the difference between graphs. The whole class came to a conclusion that it was the steepness of the graph that showed the difference, because the steeper the graph, the greater the rate of change is. Then Mr. Cooper briefly reviewed with us about how we could tell if a set of numbers was linear by looking at it's table. To summarise that, it was that you have to find patterns between the x axis numbers and the y axis numbers.

__**Problem 2.4**__ Race- 100 meters Emile- 2.5 meters/1 second = 100/2.5= 40= It would take him 40 seconds to finish Henri- 1 meter/1 second= 100/1=100= It would take him 100 seconds to finish 65 meter head start= Henri to finish in 35 second and Emile would finish in 40 second
 * Emile knows that his brother would enjoy winning the race, but he does not want to make the race so short that it is obvious his brother will win.**
 * What would be a good distance to make the race so that Henri will win in a close race? Describe your strategy, and give evidence to support your answer.**

If the race was 100 meters, which is a good distance for a race, then Henri should get a 65 meter head start. The reason is, Henri walks a meter a second, while Emile walks 2.5 meters a second. It would take Emile 40 seconds to finish a 100 meter race, while it would take Henri 100 seconds to finish a 100 meter race. If Emile gives Henri a 65 meter head start, then at his rate, Henri will finish the race in 35 seconds, while it would take Emile 40 seconds to finish the race if he were to start from 100 meters away from the finish line. So, in the end, Henri would come 5 seconds before Emile which is a pretty close race.

A good distance would be to give his brother a 55 meter head start, because like I explained in the problem before, from a 65 meter head start it would take Henri 35 seconds to finish, while from a 55 meter head start it would take Henri 45 seconds, because you are giving him 10 meters less of a head start. If that were to happen, then Emile would finish 5 seconds before Henri, and that makes it a pretty close race.
 * __Problem 2.4 Follow-Up__**
 * What would be a good distance to choose if Emile wants to beat his brother, but wants the race to be close? Explain.**