Question 1138064
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<pre>
Let x = the speed of the faster car, in mph

Then the speed of the slower car is (x-10) miles per hour.


From the condition, you have this "time" equation


    {{{100/(x-10)}}} - {{{100/x}}} = {{{5/6}}}   of an hour


To solve it, multiply both sides by  6x*(x-1).  You will get


    600*x - 600*(x-10) = 5x*(x-10).


    6000 = 5x^2 - 50x


    5x^2 - 50x - 6000 = 0


    x^2 - 10x - 1200 = 0


    (x-40)*(x+30) = 0.


The roots are 40 and -30.  Only positive root is meaningful.


<U>ANSWER</U>.  The faster car speed is 40 mph.


<U>CHECK</U>.   The faster car spends  {{{100/40}}} = {{{10/4}}}  hours.

         The slower car spends  {{{100/30}}} = {{{10/3}}}  hours.

         The difference is  {{{10/3 - 10/4}}} = {{{40/12 - 30/12}}} = {{{10/12}}} = {{{5/6}}} of an hour.   ! Correct !
</pre>

Solved and completed.


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From my post learn on how to write, to solve and to use the "time" equation.