Machine X and Y work at their respective constant rates. How many

Machine 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?

1. Machine X and Y, working together, fill a production order of this size in two thirds the time that Machine X does.
2. Machine Y, working alone, fills a production order of this size in twice the time that Machine X, working alone, does.

Let x and y represent the respective rates of X and Y.
We must know the values of both x and y to know “how many more hours”. In other words, y = 2x does not tell us how many more hours the job takes Y than X, only that Y takes twice as long. If x = 2, y = 4 and the difference is 2. However, if x = 3, y = 6, and it now takes 3 hours longer.

1) 1/x + 1/y = 1/T
So, T (total time) = xy / (x+y)
Statement 1 tells us that the total time or combined = 2/3 x
So, xy / (x+y) = 2/3 x
Solve and you get y = 2x
INSUFFICIENT – again, it only gives us a relationship

2) translated gives y = 2x

Statements 1 and 2 provide the same information, so either D or E
Since we cannot combine 2 similar equations to solve for 2 variables, the answer is E