SOLUTION: When driving a 9 hour trip home, Sharon drove 420 miles on the interstate and 135 miles on country roads. Her speed on the interstate was 25 more than on country roads. What was he

                SPEED       TIME           DISTANCE

INTERST         r+25        420/(r+25)     420

COUNTRY         r           135/r          135

TOTAL                       9

Let r = her speed, in miles per hour , on country roads.


Then the other speed is  (r+25) mph.


You have this  "time" equation


     +  = 9  hours.           <<<---=== Every fraction on the left side is the time to cover the distance . . . 


To solve it, multiply both sides by  r*(r+25).


     420r + 135*(r+25) = 9r*(r+25).


Now simplify and solve this quadratic equation.


     420r + 135r + 135*25 = 9r^2 + 9*25r

     9r^2 - 330r - 3375 = 0

     3r^2 - 110r - 1125 = 0

      r =  = .


Only positive root is meaningful  r =  =  = 45.


ANSWER.  45 miles per hour.


CHECK.    +  =  +  = 6 + 3 = 9 hours.   ! Correct !