Question 311811
Working together, Rick and Juanita can complete a job in 6 hours.
 It would take Rick 9 hours longer than Juanita to do the job alone.
 How long would it take Juanita alone?
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Let t = time for J to do it alone
then
(t+9) = time for R to do it alone
:
Let the completed job = 1
:
A shared work equation:
{{{6/t}}} + {{{6/(t+9)}}} = 1
Multiply equation by t(t+9), results
6(t+9) + 6t = t(t+9)
:
6t + 54 + 6t = t^2 + 9t
combine on the right
0 = t^2 + 9t - 12t - 54
:
t^2 - 3t - 54 = 0
Factor
(t-9)(t+6) = 0
positive solution
t = 9 hrs J, alone
then
9 + 9 = 18 hrs R alone
:
:
Check solution
6/9 + 6/18 = 1

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Note: Rick only has one arm