Question 1173385
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It takes Erica 50 min to drive to work in the morning. She drives home using the same route, 
but it takes 21 min longer, and she averages 16 mi/h less than in the morning. How far does Erica drive to work?
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<B>Solution</B>


<pre>
Let "d" be the one way distance, in miles (the value under the problem's question).



Driving to work is 50 minutes;  the average rate is  {{{d/50}}}  miles per minute.

Driving back    is 71 minutes;  the average rate is  {{{d/71}}}  miles per minute.



The difference of the average rates is  {{{d/50}}} - {{{d/71}}}  miles per minute.

According to the condition, this difference is  16 miles per hour,  or  {{{16/60}}}  miles per minute.



So, you have this equation


    {{{d/50}}} - {{{d/71}}} = {{{16/60}}}.



To solve it, multiply both sides by 50*71*60. You will get


    60*71*d - 60*50*d = 16*50*71

    (60*71 - 60*50)*d = 16*50*71


           d          = {{{(16*50*71)/(60*71-60*50)}}} = 45.079.


<U>ANSWER</U>.  One-way distance is  45.079 miles.
</pre>

Solved.