Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?Let

x and

y be the times needed for machines X and Y respectively working alone to fill a production order of this size.

Question:

y-x=?(1) Machines X and Y, working together, fill a production order of this size in 2/3 the time that machine X, working alone, does --> general relationship:

\frac{1}{x}+\frac{1}{y}=\frac{1}{total \ time} --> Total time needed for machines X and Y working together is

total \ time=\frac{xy}{x+y} (general formula) --> given

\frac{xy}{x+y}=x*\frac{2}{3} -->

2x=y. Not sufficient

(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does -->

2x=y, the same info. Not sufficient

(1)+(2) Nothing new. Not Sufficient.

Answer: E.

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