SOLUTION: Working together bob and dan complete a job in 6 hours. It would take Bob 9 hours longer than Dan to do the job alone. How long would it take Dan alone

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Question 1119370: Working together bob and dan complete a job in 6 hours. It would take Bob 9 hours longer than Dan to do the job alone. How long would it take Dan alone
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
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%2Fd + 1%2F%28d%2B9%29 = 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.   1%2F9 + 1%2F%289%2B9%29 = 1%2F9 + 1%2F18 = 2%2F18 + 1%2F18 = 3%2F18 = 1%2F6.   ! Correct !

Solved.

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