Question 1160587
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<pre>

Let "w" be her rate walking, in km/h.

Then the biking rate is (w+8) km/h.


From the condition you have this equation


    {{{(25/60)*(w+8)}}} = {{{(75/60)*w}}}


saying that the distance is the same in both directions.


From the equation (canceling 60 in the denominators)


    25*(w+8) = 75w

    w + 8 = 3w

    8 = 3w - w = 2w

    w = 8/2 = 4 km/h.


So, the walking rate is 4 km/h;  then the (walking) distance is  {{{(5/4)*4}}} = 5 kilometres.    <U>ANSWER</U>
</pre>

<U>Another solution</U>


<pre>
Let "d" be the distance under the question.


Then from condition you have this equation, connecting rates


    {{{d/25}}} - {{{d/75}}} = {{{8/60}}}  kilometres per minute.


Simplify by canceling factor 5 in denominators

    {{{d/5}}} - {{{d/15}}} = {{{8/12}}} = {{{2/3}}}.


Multiply both sides by 15


    3d - d = 10

    2d     = 10

     d     = 10/2 = 5 kilometres,


and you get the <U>same</U> answer for the distance.
</pre>

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Solved two times by different methods for your better understanding.