SOLUTION: Eva can paint three rooms in seven hours. Eva and Anna working together can paint four rooms in nine hours. How long would it take Anna to paint two rooms on her own? I used t

Question 107678: Eva can paint three rooms in seven hours. Eva and Anna working together can paint four rooms in nine hours. How long would it take Anna to paint two rooms on her own?
I used the equation 3/7 + 2/X = 4/9. Rooms/ Hours. Then got a common Denominator of 63X. Came up with 2 rooms in 126 Hours. Doesn't seem right. I have asked every one I know and they all come up with a different answer. Am I setting up the equation right? X=126 makes this equation work but seems un logistic.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I really admire the fact that you considered whether your answer made sense or not. At first glance, it doesn't seem logical to me either, but wait...

Consider how long it would take Eva to paint the 4 rooms by herself. Since she does 3 rooms in 7 hours, she paints 1 room in hour. Therefore she should be able to paint 4 rooms in hours.

But Eva and Anna together take 9 hours to paint the 4 rooms. That means that Anna's contribution to the work is very small, i.e. she only reduced the elapsed time by 20 minutes. That tells me that Anna works VERY slowly, so 63 hours per room or 126 hours for 2 rooms is not an unreasonable result after all.

What might be considered illogical is if Anna keeps her job as a painter. Myself, I'd fire her and hire another Eva.
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