Question 1132341
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            The post by @josgarithmetic contains mistake and leads you to  NOWHERE.


            I came to fix his error and provide the correct solution.



<pre>
Let "r" be the speed (in miles per hours) he drove the first 25 miles; then the time to cover this distance was  {{{25/r}}}  hours.


The speed he drove the last 65 miles was (r+15) miles; and the time to cover this distance was  {{{65/(r+15)}}}  hours.


The "time" equation is  


{{{25/r}}} + {{{65/(r+15)}}} = 1.5  hours.


Multiply both sides by  2*r*(r+15)  and simplify.  You will get the quadratic equation


{{{r^2 - 45r - 250}}} = 0.


Factor left side


(r-50)*(r+5) = 0.


Of two roots, only positive root  r= 50 is meaningful.


It is your answer:  r= 50 miles per hour was the speed he drove during the first 25 miles.


<U>CHECK</U>.   {{{25/50}}} + {{{65/(50+15)}}} = {{{1/2}}} + 1 = {{{1}}}{{{1/2}}} hours.   ! Precisely correct !
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Solved.