Question 1137736
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<pre>
Let x be his average speed (in km/h).


Then from the condition you have this  "time"  equation


    {{{200/x}}} - {{{200/(x+2)}}} = 0.25   of an hour   (0.25 = 0.25 hour = 15 minutes)


To solve it, first multiply both sides by  4x*(x+2).  You will get


    800*(x+2) - 800x = x*(x+2)


    1600 = x*(x+2)


    x^2 + 2x - 1600 = 0


    {{{x[1,2]}}} = {{{(-2 +- sqrt((-2)^2 + 4*1600))/2}}} = {{{(-2 +- sqrt(6404))/2}}} = {{{-1 +- sqrt(1601))/2}}}.


Of the two roots, only positive root x= {{{-1 + sqrt(1601)}}} = 39.0125 is meaningful.


<U>Answer</U>.  His average speed is 39.0125 km/h  (approximately).


<U>CHECK</U>.   {{{200/39.0125}}} - {{{200/(39.0125 + 2)}}} = 0.25.    ! Correct !
</pre>

Solved.