Question 1137496
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Let x be the Kim's rate (the slower sister) in miles per hour.

Then the faster sister's rate is (x+3) miles per hour.



Karin spent {{{12/(x+3)}}} hours running.

Kim    spent  {{{8/x}}}  hours walking.



The condition says


    {{{12/(x+3)}}} = {{{8/x}}}.


It is your basic equation.

It is called "time" equation, because its both sides represent time spent.



To solve the equation, cross multiply.  You will get


    12x = 8((x+3)

    12x = 8x + 24

    12x - 8x = 24

     4x      = 24

      x      = 24/4 = 6.


<U>Answer</U>.  Kim's rate is 6 miles per hour;  Karin's rate is 6+3 = 9 miles per hour.
</pre>

Solved.


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From my solution learn how to use, how to write and how to solve a "time" equation.