Question 206584
Rick and Maura work together ans sew a quilt in 4 hrs.
 Working alone Maura would need 6 hrs more than Rick to sew the quilt.
 How long would it take each if they worked alone?
:
Let t = time required by Rick alone
then
(t+6) = Maura alone
:
Let the completed quilt = 1
:
{{{4/((t+6))}}} + {{{4/t}}} = 1
Multiply equation by t(t+6) to get rid of the denominators, results
:
4t + 4(t+6) = t(t+6)
:
4t + 4t + 24 = t^2 + 6t
:
8t + 24 = t^2 + 6t
:
Arrange as a quadratic on the right
0 = t^2 + 6t - 8t - 24
:
t^2 - 2t - 24 = 0
Factors to:
(t-6)(t+4) = 0
:
positive solution
t = 6 hrs, is Rick's time alone
and
6 + 6 = 12 hrs Maura's time alone 
:
:
Check solution in original equation
{{{4/12}}} + {{{4/6}}} = 
{{{2/6}}} + {{{4/6}}} = 1