Question 429498
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Two runners start at a certain point simultaneously, going the same directions, the speed for one runner is two thirds 
of the speed of the other runner. If at the end of 3 hours they are 6 miles apart, what is the speed of each runner?
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        The solution of the other tutor is incorrect.

        I came to bring a correct solution.



<pre>
Let x be "One" runner speed, in mph.

Then the "other" runner speed is  {{{(3/2)x}}} mph  <<<---===  it is the true meaning of the problem's condition.


The "distance " equation is

    {{{3*((3/2)x)}}} - {{{3x}}} = 6  miles  (the difference of the ran distances in 3 hours)


Simplify and find x

    {{{(9/2)x}}} - 3x = 6,

    9x - 6x = 12,

       3x   = 12,

        x   = 12/3 = 4.


<U>Answer</U>.  The slower runner' speed is 4 mph.  The faster runner' speed is  {{{(3/2)*4}}} = 3*2 = 6 mph.
</pre>

Solved correctly.