SOLUTION: Mutt and Jeff need to paint a fence. Mutt can do the job alone 6 hours faster than Jeff. If together they work for 14 hours and finish only of the job, how long would Jeff need to

Question 347507: Mutt and Jeff need to paint a fence. Mutt can do the job alone 6 hours faster than Jeff. If together they work for 14 hours and finish only of the job, how long would Jeff need to do the job alone?
Your answer must be a number. No arithmetic operations are allowed.
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
The setup on this one is

where M and J are the times it would take each person alone and t is the amount of time they work together. The 1 represents the whole job, but now that I look at your problem, that fact is missing...here's how it would go if it were a 1...
Here M = J - 6 so our equation becomes

To solve this, multiply by the LCD, which is J(J - 6), and get
14J + 14(J - 6) = J(J - 6)
14J + 14J - 84 = J^2 - 6J
Consolidating, we get
J^2 - 34J - 84 = 0
and go from there...
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