Question 602226
Larry and Margee can paint a room in 7 hours.
 If Margee worked alone it would take her 3 hours longer than if Larry worked alone.
 How long would it take each person if they worked alone?
:
Let t = L's time to do the job alone
then
(t=3) = M's time to do it
:
Let completed job = 1 (a painted room)
:
{{{7/t}}} + {{{7/((t+3))}}} = 1
:
Multiply by t(t+3) to clear the denominators, results
7(t+3) + 7t = t(t+3)
7t + 21 + 7t = t^2 + 3t
14t + 21  = t^2 + 3t
0 = t^2 + 3t - 14t - 21
A quadratic equation
t^2 - 11t - 21 = 0
use the quadratic formula to find t
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In this equation: x=t; a=1; b=-11; c=-21
{{{t = (-(-11) +- sqrt(-11^2-4*1*-21 ))/(2*1) }}}
:
{{{t = (11 +- sqrt(121+84 ))/2 }}} 
:
{{{t = (11 +- sqrt(205 ))/2 }}} 
The positive solution
{{{t = (11 + 14.3)/2 }}}
t = {{{25.3/2}}}
t = 12.65 hrs, time L takes working alone
then
12.65+3 = 15.65 hrs, time M takes working alone