Question 1162900
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<pre>

Let x be the Edward's rate driving, in miles per hour.


Then the Kate's rate driving is  (x+8) mph.


Write the "time" equation


    {{{112/x}}} - {{{112/(x+8)}}} = {{{1/4}}}   of an hour.


To solve it, multiply both sides by 4x*(x+8).  You will get


    112*4*(x+8) - 112*4*x = x*(x+8)

    112*4(x+8) - 112*4x = x*(x+8)

    3584 = x*(x+8)      (*)


From this point, there are two ways to complete the solution.


First way is to solve this quadratic equation formally.
In this way, you will get the <U>ANSWER</U> 56 mph for Edwards and 64 mph for Kate.


The other way is to introduce new variable y = x+4.
Then x+8 = y-4,  and your equation (*)  takes the form

    3584 = (y-4)*(y+4)

    3584 = y^2 - 16

    3584 + 16 = y^2  

    3600 = y^2

    y  =  60


and you get the same answer practically MENTALLY.
</pre>

Solved.