Let d = "How long would it take Dan alone".


Then the time for Bob working alone is (d+9) hours.


The equation for "d" is this


     +  = 1/6            (1)


saying that the two rates of work sum up to 1/6 of the job per hour.


From (1) you get step by step


    6*(d+9) + 6d = d*(d+9) 

    6d + 54 + 6d = d^2 + 9d

    d^2 - 3d - 54 = 0

    (d+6)*(d-9) = 0.


The only positive root is d = 9.


Answer.  Dan needs 9 hours to complete the job alone.


Check.    +  =  +  =  +  =  = .   ! Correct !