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?
(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.
(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.
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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) = x
