SOLUTION: Sheri drove southeast from Albuquerque to Roswell and then south to Carlsbad. She averaged 75 MPH along the route from Albuquerque to Roswell and averaged 70 MPH from Roswell to Ca

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Sheri drove southeast from Albuquerque to Roswell and then south to Carlsbad. She averaged 75 MPH along the route from Albuquerque to Roswell and averaged 70 MPH from Roswell to Ca      Log On


   

Question 148128: Sheri drove southeast from Albuquerque to Roswell and then south to Carlsbad. She averaged 75 MPH along the route from Albuquerque to Roswell and averaged 70 MPH from Roswell to Carlsbad. She covered the entire 220 miles in 3 hours. How long did she take to drive from Albuquerque to Roswell?
I started by making a table
DISTANCE RATE TIME
270 75 3hrs
270 70 3hrs
but the problems that I was coming up with did not make sense to me. Am I going about thie correctly?
Found 2 solutions by vleith, checkley77:
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
You need to break the trip into two parts.
The total trip is 220. The total time is 3 hours.
Let the distance from Albuquerque to Roswell be x (watch out for aliens in Roswell).
Then the distance from Roswell to Carlsbad is 220+-x
The time for each leg is given by distance%2Fspeed+=+time
The time to Roswell is x%2F75
The time to Carlsbad is %28220-x%29%2F70
The total time is 3 hours.
3+=+x%2F75+%2B+%28220-x%29%2F70
3+=+x%2F75+%2B+220%2F70+-+x%2F70
3+-+%28200%2F70%29+=+x%2F75+-+x%2F70+
%28%28210+-+220%29%2F70%29+=+%2870x+-+75x%29%2F%2870%2A75%29+
%28%2870%2A75%29%2A%28-10%2F70%29%29+=+-+5x
-750+=+-5x
150+=+x
So the distance to Roswell is 150 miles.
At an average speed of 75 mph, the drive to roswell takes 2 hours.

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
220=75x+70(3-x)
220=75x+210-70x
220=5x+210
5x=220-210
5x=10
x=10/5
x=2 hours driving @ 75 mph.
3-2=1 hour driving @ 70 mph.
proof
220=75*2=70*1
220=150+70
220=220
75*2=150 miles from Albuquerque to Roswell.