SOLUTION: Justin recently drove to visit his parents who live 864 miles away. On hi way there his average speed was 21 miles per hour faster than on his way home. If Justin spent a total of

Question 1074799: Justin recently drove to visit his parents who live 864 miles away. On hi way there his average speed was 21 miles per hour faster than on his way home. If Justin spent a total of 24 hours driving, find the two rates.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
speed there was x+21 mph and time was 864/x+21hours. S*t=distance
speed back was (x) mph and time was 864/x hours.
The two times add to 24
so 864/x+864/(x+21)=24
multiply both sides by x(x+21)
864(x+21)+864(x)=24(x(x+21))
864x+18144+864x=24x^2+504x
0=24x^2-1224x-18144
divide by 24
x^2-51x-756=0
(x-63)(x+12)=0
x=63 mph, only positive root speed back, which took 864/63 or 13.71 hours.
x+21=84 mph, which took 10.29 hours there.
Total is 24 hours.

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