fambrini wrote:Machine X and machine Y, working at the same time, produce w widgets in k hours. Machines A, B and C, together produce w widgets in k - 2 hours. If all the machines have the same productivity, what is the value of K?
A) 2
B) 3
C) 6
D) 8
E) 9
Let the rate for each machine = 1 widget per hour.
Combined rate for X and Y = 2 widgets per hour.
Combined rate for A, B and C = 3 widgets per hour.
At a rate of 2 widgets per hour, the amount of work produced by X and Y in k hours = rt = 2k.
At a rate of 3 widgets per hour, the amount of work produced by A, B and C in k-2 hours = rt = 3(k-2) = 3k-6.
Since the amount of work in each case is THE SAME, we get:
2k = 3k-6
6 = k.
The correct answer is
C.
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