ALGEBRA 2
posted by Emily .
Mrs. Smith drove at a rate of 45 mi/h from her home to her sister's house. She spent 1.5 hours having lunch with her sister. She then drove back home at a rate of 55 mi/h. The entire trip, including lunch, took 4 hours. How far does Mrs. Smith live from her sister?
I set it up like this: 45t+55t=2.5 hours
I got she lives 100 miles but I don't know for sure if I did it right. If someone could check my work I would love it. Thanks in advance.

I do not get 100 miles.
Here is a better way to set up the equation:
let d = the distance between the two houses.
The total time is 4 hours. The time spent traveling can be found by manipulating V = d/t
t = d/V
So the time is the displacement divided by the velocity.
45/d + 55/d + 1.5 = 4
d = ? 
40 miles