Question 676202
Let {{{ t }}} = Michelle's time in hrs  to stain deck
{{{ t + 6 }}} = Shawn's time in hrs to stain deck
Add their rates of working to get rate working together
( 1 deck stained ) / ( Shawn's time ) + ( 1 deck stained ) / ( Michelle's time ) = rate working together
{{{ 1 / ( t + 6 ) + 1/t = 1 / 1.6 }}}
Multiply both sides by {{{ 1.6*( t + 6 )*t }}}
{{{ 1.6t + ( t + 6 )*1.6 = t*( t + 1.6 ) }}}
{{{ 1.6t + 1.6t + 9.6 = t^2 + 1.6t }}}
{{{ 1.6t + 9.6 = t^2 }}}
{{{ t^2 - 1.6t - 9.6 = 0 }}}
Use quadratic formula
{{{ t = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -1.6 }}}
{{{ c = -9.6 }}}
{{{ t = (-(-1.6) +- sqrt( (-1.6)^2 - 4*1*(-9.6) )) / (2*1) }}}
{{{ t = ( 1.6 +- sqrt( 2.56 + 38.4 )) / 2 }}}
{{{ t = ( 1.6 +- sqrt( 40.96 )) / 2 }}}
{{{ t = ( 1.6 + 6.4) / 2 }}} ( ignore the negative square root )
{{{ t = 8/2 }}}
{{{ t = 4 }}}
{{{ t + 6 }}} = Shawn's time, so
{{{ t + 6 = 10 }}}
Shawn takes 10 hrs to stain deck by himself