Question 891733
(1) Carl's rate of painting added to Jennifer's rate
of painting equals their rate of painting when
they work together
(2) Carl's rate is known, and so is their rate when
working together, so Jennifer's rate can be found
(3) Let Jennifer's rate = ( 1 room painted ) / ( t hours )
(4) Carl's rate = ( 1 room painted ) / ( ( t - 3 ) hours )
(5) Working together, their rate = ( 1 room painted ) / ( 2 hours )
(6) The equation is:
{{{ 1 / ( t-3 ) + 1/t = 1/2 }}}
(7) Multiply both sides by {{{ 2t*( t-3 ) }}}
(8) {{{ 2t + 2*( t-3 ) = t*( t-3 ) }}}
(9) {{{ 2t + 2t - 6 = t^2 - 3t }}}
{{{ t^2 - 7t + 6 = 0 }}}
(10 ) Use the quadratic formula to solve for {{{ t }}}, Jennifer's time