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(52784) (Show Source):
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 !
