Question 1138796
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Let x be the rate on the first part of the trip, in miles per hour.

Then the rate on the second part was  (x+10) mph, according to the condition.


The time to travel the first part  was  {{{21/x}}}  hours.

The time to travel the second part was  {{{21/(x+10)}}}.


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


    {{{21/x}}} + {{{21/(x+10)}}} = {{{80/60}}},  or


    {{{21/x}}} + {{{21/(x+10)}}} = {{{4/3}}}  hours.


To solve the equation, multiply both sides by 3x*(x+10).  You will get


    63*(x+10) + 63*x = 4x*(x+10).


Simplify it step by step and solve 


    63x + 630 + 63x = 4x^2 + 40x

    4x^2 - 86x - 630 = 0

    2x^2 - 43x - 315 = 0


Solve this quadratic equation and take its positive root.
It will be your solution/answer. 
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