Walkabout wrote:
Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y)
(B) y/(x+y)
(C) xy/(x+y)
(D) xy/(x-y)
(E) xy/(y-x)
I went through so many solutions and I'm surprised nobody mentioned that this question could've simply been done by option elimination.Since we have been given that x and y have their units as hours, we can clearly eliminate options A and B as they result in unitless quantities.
The amount of time it takes B to produce 800 nails cannot be a unitless quantity, it has to have its unit as hours. Eliminate options A and B.Notice that by simple observation we can see that y is greater than x, because it obviously would take machine A more number of hours (y) than it takes for both of them to produce the same number of nails (x).
This brings us to option D. Option D has a denominator that results in an overall negative value. Eliminate D.Between C and E, we know that it is the
addition of the rates of working of machines A and B that will result in them producing given number of nails.
So if we are to determine the rate of one machine alone, there has to be a subtraction involved of the other machine's rate from their overall rate. Option C presents us with a quantity that has no subtraction involved. Clearly wrong.Hence, our answer is option E.Posted from my mobile device