Question 210858
(Cindt's rate) + (Eva's rate) = Rate working together
actually they worked together for 6 of the 8 hours
and Cindy worked 2 hours alone
Let {{{t}}}= hours it takes Cindy to finish 1 payroll
{{{t + 3}}}= hours for Eva to finish 1 payroll
Let {{{p}}}= fraction of payroll completed in 6 hours
with both working together
{{{1/t + 1/(t+3) = p/6}}}
And Cindy working alone for 2 hours:
{{{1/t = (.9 - p)/2}}}
{{{.9 - p = 2/t}}}
{{{-p = 2/t - .9}}}
{{{p = .9 - 2/t}}}
and
{{{1/t + 1/(t+3) = .9/6 - 2/(6t)}}}
Multiply both sides by {{{6t*(t+3)}}}
{{{6*(t+3) + 6t = .15*6t*(t+3) - 2*(t+3)}}}
{{{8*(t+3) + 6t = .15*6t*(t+3)}}}
{{{8t + 24 + 6t = .15*6t*(t+3)}}}
{{{14t = .9t^2 + 2.7t - 24}}}
{{{.9t^2 - 11.3t - 24 = 0}}}
{{{9t^2 - 113t - 240 = 0}}}
Use quadratic equation
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 9}}}
{{{b = -113}}}
{{{c = -240}}}
{{{t = (-(-113) +- sqrt( (-113)^2-4*9*(-240) ))/(2*9) }}}
{{{t = (113 +- sqrt( 12769 + 8640 ))/18 }}}
{{{t = (113 +- sqrt( 21409 ))/18 }}} 
{{{t = (113 +- 146.32)/18 }}}
{{{t = 14.4}}} hrs
They have 10% of the job left
{{{1/t + 1(t+3) = .1/T}}}
{{{1/14.4 + 1/17.4 = .1/T}}}
{{{.0694 + .0575 = .1/T}}}
{{{T = .1/.12687}}}
{{{T = .788}}}hrs
It will take them about 47.3 min to finish the job
(Unless I goofed)