SOLUTION: jon recently drove to visit his parents who live 675 miles away. on his way there his average speed was 24 mph faster than on his way home. if jon spent a total of 30 hours driving

Algebra ->  Rational-functions -> SOLUTION: jon recently drove to visit his parents who live 675 miles away. on his way there his average speed was 24 mph faster than on his way home. if jon spent a total of 30 hours driving      Log On


   

Question 841113: jon recently drove to visit his parents who live 675 miles away. on his way there his average speed was 24 mph faster than on his way home. if jon spent a total of 30 hours driving find the two rates.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
jon recently drove to visit his parents who live 675 miles away. on his way there his average speed was 24 mph faster than on his way home. if jon spent a total of 30 hours driving find the two rates.
----------
To DATA:
distance = 675 miles: rate = r+24 mph ; time = d/r = 675/(r+24) hours
------
From DATA:
distance = 675 miles ; rate = r mph ; time = 675/r hrs
---------
Equation:
time + time = 30 hrs.
-----------------------------
675/r + 675/(r+24) = 30 hrs
675r + 675*24 + 675r = 30r(r+24)
--------
1350r + 675*24 = 30r^2 + 30*24
------
30r^2 - 1350r - 645*24 = 0
3r^2 - 135r - 129*12 = 0
r^2 - 45r - 129*4 = 0
----
Positive solution:
rate coming home = 54.47 mph
rate going = 30.47
--------
Cheers,
Stan H.
-----------------