SOLUTION: Dale and Roger complete a job in 6 hours. It would take Dale 9 hours longer than Roger to do the job alone. How long would it take Roger alone? my teacher got 9hours but im not get

Question 707434: Dale and Roger complete a job in 6 hours. It would take Dale 9 hours longer than Roger to do the job alone. How long would it take Roger alone? my teacher got 9hours but im not getting 9hrs.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let x = time it takes for Roger to do the job alone

So x+9 = time it takes for Dale to do the job alone

1/x + 1/(x+9) = 1/6

x+9/(x(x+9)) + x/(x(x+9)) = 1/6

(x+9 + x)/(x(x+9)) = 1/6

(2x+9)/(x(x+9)) = 1/6

6(2x+9) = 1*x(x+9)

12x + 54 = x^2 + 9x

0 = x^2 + 9x - 12x - 54

x^2 - 3x - 54 = 0

(x - 9)(x + 6) = 0

x-9 = 0 or x+6 = 0

x = 9 or x = -6

Ignore the negative answer.

So Roger can do the job in 9 hours if he does it alone

Dale can do the job in 18 hours if he does it alone

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