SOLUTION: Koko can paint a room two hours less than Andre. If they will work together, they can finish the job in 12 hours. How long would it take each person to complete the same job workin

Question 890914: Koko can paint a room two hours less than Andre. If they will work together, they can finish the job in 12 hours. How long would it take each person to complete the same job working alone?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!
Koko can paint a room two hours less than Andre.

Suppose Andre cn paint a room in x hours.

Then Koko can pain a room in x-2 hours

So Andre's painting rate is 1 room per x hours or  or 

And Koko's painting rate is 1 room per x-2 hours or  or

If they will work together, they can finish the job in 12 hours.

So their combined painting rate is 1 room per 12 hours or  or 

The equation comes from 

          

     

Multiply through by LCD of 12x(x-2)

   

   x^2-2x}}}

        x^2-2x}}}

           

That doesn't factor, so

          

          

          

          

Solutions x=25.04159458 and 0.9584054212

The second answer makes no sense since (1) we can't subtract 2 from it and
get a positive answer, and (2) if Andre being able to finish in less than 
an hour makes no sense. :)

Answer:  It would take Andre a little over 25 hours and Koko a little 
over 23 hours.

Edwin

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