Question 518246
The position of car B relative to car A's
starting point is {{{ 10 - 40t }}} km
The position of car A relative to it's
own starting point is {{{ 30t }}}
The distance between A and B is
{{{ sqrt( ( 10 - 40t )^2 + ( 30t )^2 ) }}}
{{{ sqrt( 100 - 800t + 1600t^2 + 900t^2 ) }}}
{{{ sqrt( 2500t^2 - 800t + 100 ) }}}
The minimum value occurs at {{{ t = -b/(2a) }}}
{{{ a = 2500 }}}
{{{ b = -800 }}}
{{{ t = -(-800)/5000 }}}
{{{ t = 8/50 }}
{{{ t = 4/25 }}}
{{{ (4/25)*60 = (4/5)*12 }}}
{{{ 48/5 = 9.6 }}}
They will be closest to each other in 9.6 minutes
Hope I got it