Question 1136208
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<pre>
Let r = her speed, in miles per hour , on country roads.


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


You have this  "time" equation


    {{{420/(r+25)}}} + {{{135/r}}} = 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 = {{{(110 +- sqrt(110^2 + 4*3*1125))/(3*2)}}} = {{{(110 +- 160)/6}}}.


Only positive root is meaningful  r = {{{(110 + 160)/6}}} = {{{270/6}}} = 45.


<U>ANSWER</U>.  45 miles per hour.


<U>CHECK</U>.   {{{420/(45+25)}}} + {{{135/45}}} = {{{420/70}}} + {{{135/45}}} = 6 + 3 = 9 hours.   ! Correct !
</pre>

Solved.


Using &nbsp;"time" &nbsp;equation is the &nbsp;STANDARD &nbsp;way to solve such problems.


From this solution, &nbsp;learn on how to write, &nbsp;how to use and how to solve a &nbsp;"time" &nbsp;equation.


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