Question 549564
Let {{{ t }}} = Wilma's time to do the job working alone
{{{ t - 2 }}} = Lilly's time working alone
Add their rates of working to get their
rate working together
( 1 job / t hrs ) + ( 1 job / t-2 hrs ) = rate working together
{{{ 1/t + 1/(t-2) = 1/(4/3) }}}
{{{ 1/t + 1/(t-2) = 3/4 }}}
Multiply both sides by {{{ t*(t-2)*4 }}}
{{{ 4*(t-2) + 4t = 3t*(t-2) }}}
{{{ 4t - 8 + 4t = 3t^2 - 6t }}}
{{{ 3t^2 - 14t + 8 = 0 }}}
Use quadratic equation to solve
{{{ t = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}} 
{{{ a = 3 }}}
{{{ b = -14 }}}
{{{ c = 8 }}}
{{{ t = (-(-14) +- sqrt( (-14)^2 - 4*3*8 ))/(2*3) }}} 
{{{ t = ( 14 +- sqrt( 196 - 96 ))/6 }}} 
{{{ t = ( 14 + sqrt(100) )/ 6 }}}
{{{ t = ( 14 + 10 )/ 6 }}}
{{{ t = 4 }}}
and, also
{{{ t = 2/3 }}}
I can't use {{{ 2/3 }}} because I have to subtract {{{2}}}
and I can't have negative time
{{{ t = 4 }}}
{{{ t - 2 = 2 }}}
4 hrs = Wilma's time to do the job working alone
2 = Lilly's time working alone
check answers:
{{{ 1/t + 1/(t-2) = 3/4 }}}
{{{ 1/4 + 1/2 = 3/4 }}}
{{{ 3/4 = 3/4 }}}
OK