3) Recall problem 48 from your notes: Half an hour after leaving her house, Leah was 25 miles from
home. Leah then merged onto the freeway, and was able to travel at a constant speed for the next
several hours. Four hours after leaving her house, she was 280 miles from home.
a.
Find the model, m(t) that gives Leah's distance from home d in terms of the number of hours
she has been on the freeway, t.
b.
Suppose that Rachel lives 5 miles away from the same freeway entrance that Leah took. Rachel
leaves her house, and 10 minutes later is on the freeway. After 3.7 hours, Rachel is also 280 miles
away from her home.
i. What is Rachel's average speed on the freeway?
ii. Suppose that Rachel travels at a constant speed once she gets on the freeway. Write a
function k = f(t) that describes the number of miles she is from home, k, in terms of
the number of hours since she left home, t.
c. Assuming they are both traveling at a constant rate, who is driving faster? Give two different
answers to how you can see this
i. intuitively from the information provided.
ii. Algebraically from how you defined the functions.