SOLUTION: working together , rick and jaunita can complete a job in 6 hrs. it would take rick 9 hrs longer than juanita to do the job alone. how long would it take juanita alone? what

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Question 541124: working together , rick and jaunita can complete a job in 6 hrs. it would take rick 9 hrs longer than juanita to do the job alone. how long would it take juanita alone? what i did was x= the number of hours for juanita then i kind of set a chart juanita is : 1 and 1/x rick : x+9 and 1/x+9 together : is 6 hrs so 1/6 then i set a equation 1/x + 1/ x+9= 1/6 then i think we need lcd which i think is 6x(x+9) then i had trouble what to cross out. -thanks
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx+%2B+1%2F%28x%2B9%29=+1%2F6 is correct for an equation
I prefer to say that I am going to multiply both sides of the equation by the expression by 6x%28x%2B9%29. (The calculations are the same, but avoid having to write all those denominators). On multiplying, we get
%281%2Fx+%2B+1%2F%28x%2B9%29%296x%28x%2B9%29=+%281%2F6%296x%28x%2B9%29
6x%28x%2B9%29%2Fx+%2B+6x%28x%2B9%29%2F%28x%2B9%29=+%281%2F6%296x%28x%2B9%29, which simplifies to
6%28x%2B9%29+%2B+6x=+x%28x%2B9%29 --> 6x%2B54%2B6x=x%5E2%2B9x --> 12x%2B54=x%5E2%2B9x
Subtracting 12x+54 from both sides, we get
0=x%5E2%2B9x-%2812x%2B54%29 --> x%5E2%2B9x-12x-54=0 --> x%5E2-3x-54=0
That expression can be factored
%28x-9%29%28x%2B6%29=0
The solutions to that equation are x=9 and x=-6, but since x must be positive, x=9 is the only solution to the problem.
It takes Juanita 9 hours to complete the job alone.