SOLUTION: I drove to my parents' house 600 miles away. My mother worried that I drove too fast, so I promised her that when I drove home, I would slow down. I reduced my speed by 10 miles pe

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Question 763175: I drove to my parents' house 600 miles away. My mother worried that I drove too fast, so I promised her that when I drove home, I would slow down. I reduced my speed by 10 miles per hour, but the trip took 2 hours longer. How fast did I drive each way?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
Distance = rate x time.


Set up two equations for this problem. Call the unknown rate x and the unknown time t.


600 = xt


600/t = x Eq 1


The distance is the same, so the first rate times time has to equal the second rate times time, and that provides the second equation.


xt = (x-10)*(t+2) = xt +2x - 10t - 20


xt's cancel.


0 = 2x - 10t - 20 EQ 2


Substitute the x value (in terms of t) from EQ1 into EQ2


0 = 2(600/t) -10t -20 = 1200 - 10t^2 -20t


Multiply all terms by -1, so the t^2 is positive. Divide all terms by 10.


0 = t^2 + 2t -120 = (t - 10)(t+12) so t=10 or t=-12. The time of a trip cannot be negative, so discard -12.


EQ1: 600/10 = x = 60 MPH is the speed of the original trip.


The return trip was 10 MPH slower, which is 50MPH.