Question 1145951
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Let x be the average speed under the question.


Then the travel time for 660 miles distance is  {{{660/x}}} hours.


The hypothetical travel time is  {{{600/(x+6)}}}  hours.


The difference is 1 hour :


    {{{660/x}}} - {{{660/(x+6)}}} = 1  hour.


It is your basic equation, the "time" equation.


To solve it, multiply both sides by x*(x+6).  You will get


    660*(x+6) - 660x = x*(x+6).


Simplify and solve for x


    660*6 = x^2 + 6x

    x^2 + 6x - 3960 = 0

    {{{x[1,2]}}} = {{{(-6 +- sqrt(6^2 + 4*3960))/2}}} = {{{(-6 +- 125.861)/2}}}.


Only positive root makes sense  x = {{{(-6 + 126)/2}}} = 60.


<U>ANSWER</U>.  The average speed under the question is 60 miles per hour.


<U>CHECK</U>.  {{{660/60 - 660/(60+6)}}} = 11 - 10 = 1 hour.  ! Precisely correct 
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Solved.