August 22, 2006

Topics 1 1st Hour                               Name: _______________________________________________

Scenario:  During a 100 mile marathon, Kim, our champion cyclist is having struggles.  At the halfway checkpoint she is behind the leader, Allison, by 10 miles.  Kim still has a lot of energy left and is pacing herself at a constant 15 miles per hour.  Allison, on the other hand, is getting tired and has slowed down to 11 miles per hour.

a)  Think about the relationship between the distance that Kim has ridden and the number of hours since she passed the halfway checkpoint.

How far has Kim ridden 1 hour after she passes the checkpoint?

How far has Kim ridden 1.5 hours after she passes the checkpoint?

How far has Kim ridden 2 hours after she passes the checkpoint?

How far has Kim ridden x hours after she passes the checkpoint?

How can we express the relationship between KimÕs distance beyond the checkpoint and the number of hours that have elapsed?

 

 

 

b) Think about the relationship between the distance Allison has ridden and the number of hours since Kim passed the halfway point.

How far has Allison ridden when Kim passes the checkpoint?

How far has Allison ridden 1 hour after Kim passed the checkpoint?

How far has Allison ridden 2 hours after Kim passed the checkpoint?

How far has Allison ridden x hours after Kim passed the checkpoint?

 

How can we express the relationship between the distance Allison rode and the number of hours since Kim passed the checkpoint?

 

 

 

 

 

 

 

c)   In addition to looking at the location of each runner, we can look at the distance between them.

How far apart are they when the Kim is at the halfway point?

How far apart are they 1 hour later?

How far apart are they 2 hours after Kim passes the checkpoint?

How far apart are they x hours after Kim passed the checkpoint?

 

 

d) What will the distance between them be when Kim catches up to Allison completely?

 

When will this happen?

 

 

 

 

 

e)         Did Kim or Allison win the race? How do you know?