Question 957405
(1)
{{{ d = 6 }}} km
{{{ x }}} = rate in km/hr
{{{ d = x*t }}}
{{{ 6 = x*t }}}
{{{ t = 6/x }}}
--------------
(2) 
Return journey:
{{{ d = 6 }}} km
{{{ x + 3 }}} = rate in km/hr
{{{ 6 = ( x + 3 )*t }}}
{{{ t = 6/( x + 3 ) }}}
-------------------
You are given:
{{{ 6/( x+3 ) = 6/x - 20/60 }}}
( note that I converted {{{ 20 }}} min to hours )
{{{ 6/( x+3 ) = 6/x - 1/3 }}}
Multiply both sides by {{{ x*( x+3 )*3 }}}
{{{ 6*(3x)  = 6*(3*(x+3)) - x*( x+3 ) }}}
{{{ 18x = 6*( 3x + 9 ) - x^2 - 3x }}}
{{{ 18x = 18x + 54 - x^2 - 3x }}}
Subtract {{{ 18x }}} from both sides
{{{ 0 = -x^2 - 3x + 54 }}}
Multiply both sides by {{{ -1 }}}
{{{ x^2 + 3x - 54 = 0 }}}