Question 1163952
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Two persons walk towards each other on a road. It takes the first person 2 hours to walk the road, it takes the 2nd person 3 hours to walk the road. 
When they meet, the first person walked 4 and 4/5 of a mile more than the 2nd person. How long is the road?
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<pre>
Since their times to cover the entire distance are in the ratio  {{{t[1]/t[2]}}} = {{{2/3}}}, it means that their rates are in reciprocal ratio  {{{r[1]/r[2]}}} = {{{3/2}}}.

In turn, it means that going toward each other, they cover the distances, whose ratio is the same as the ratio of their speeds, i.e. {{{3/2}}}.


So, if "d" is the total one way distance, then the first person covered  {{{3/5}}}  of the distance, while the second covered  {{{2/5}}}  of the distance.


Then from the condition, you have this equation


    {{{(3/5)d}}} - {{{(2/5)d}}} = {{{4}}} {{{4/5}}}  miles,   or

   
    {{{(1/5)d}}} = {{{24/5}}} miles,

    d   = 24 miles.    <U>ANSWER</U>
</pre>

Solved.


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Notice that the solution by the tutor @htmentor is incorrect, since he incorrectly interprets the condition.