SOLUTION: Rick and Maura work together ans sew a quilt in 4 hrs. Working alone maura wiould need 6 hrs more than rick to sew the quilt. How long would it take each if they worked alone?

Question 206584: Rick and Maura work together ans sew a quilt in 4 hrs. Working alone maura wiould need 6 hrs more than rick to sew the quilt. How long would it take each if they worked alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
:
+ = 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
+ =
+ = 1

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