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?