Question 980030


Let &nbsp;<B>x</B>&nbsp; be the unknown distance &nbsp;(in kilometers).


Then the man spent &nbsp;{{{x/(2*75)}}}&nbsp; hours to cover half of the distance moving at the speed of &nbsp;75 {{{km/h}}}. 


Next, &nbsp;he spent &nbsp;{{{x/(2*45)}}}&nbsp; hours to cover half of the distance moving at the speed of &nbsp;45 {{{km/h}}}. 


The equation for the unknown distance &nbsp;<B>x</B>&nbsp; is


{{{x/(2*75)}}} + {{{x/(2*45)}}} = 12.


Solve it step by step:


{{{x/150}}} + {{{x/90}}} = 12,


{{{(3x/450)}}} + {{{(5x/450)}}} = 12,


3x + 5x = 12*450,


8x = 5400,


x = {{{5400/8}}} = 675.


<B>Answer</B>. &nbsp;The distance is &nbsp;675 km.