Question 1135051
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Let x be the rate on the way to "there", in miles per hour.

Then the rate on the way back was  (x-11) mph, according to the condition.


The time to travel "to there"  was  {{{240/x}}}  hours.

The time to travel back was  {{{240/(x-11)}}}.


The total time is the sum of these partial times, which gives you the "time" equation

    {{{240/x}}} + {{{240/(x-11)}}} = 8.


To solve the equation, first divide both sides by 8;  then multiply both sides by x*(x-11).  You will get


    30*(x-11) + 30*x = x*(x-11).


Simplify it step by step and solve 


    30x - 330 + 30x = x^2 - 11x

    x^2 - 71x + 330 = 0


Factor left side

    {x+5)*(x-66) = 0


Only positive root x= 66 is meaningful, so the answer to the problem is <U>THIS</U> :


    The rate was  66 mph on the way to parents and  66-11 = 55 pmh on the way back.


<U>CHECK</U>.  Time to travel to "there"  was  {{{240/66}}} = {{{40/11}}} hours.

        Time to travel back was  {{{240/55}}} = {{{48/11}}}  hours.

        Total time was  {{{40/11}}} + {{{48/11}}} = {{{88/11}}} = 8 hours.   ! Correct !
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Solved.


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Using "time" equation is the STANDARD way to solve such problems.


<U>The lesson to learn from my post is THREEFOLD</U>:


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    a)  Learn on <U>how to write the "time" equation</U> for such problems;
 
    b)  also learn on <U>how to solve it</U> !

    c)  also learn on <U>how to PRESENT the solution</U>.
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