Question 1170046
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Let x be that unknown regular speed under the question.


Then you have this "time" equation

    {{{270/x}}} - {{{270/(x+6)}}} = 0.5  of an hour  (or 30 minutes).     (1)



You may multiply both sides by x*(x+6); reduce to the standard form quadratic equation and then solve it to find x.



I will solve this equation MENTALLY.

For it, I will multiply both sides by 2. I will get then

    {{{540/x}}} - {{{540/(x+6)}}} = 1,


and then the solution  x= 54 becomes OBVIOUS.



<U>ANSWER</U>.  The regular speed is 54 miles per hour.


<U>CHECK</U>.  Then equation (1)  takes the form  {{{270/54}}} - {{{270/60}}} =  5 - 4.5 = 0.5  hour, confirming the answer.
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Solved.