The posted problem is the same as the following:
To produce N items, Machine A takes double the time that machine B takes. Working together at their respective rates, A and B can produce x items in 3 days. How many days will it take machine A to produce x items?
(A) 5
(B) 8
(C) 9
(D) 12
(E) 18
To produce N items, Machine A takes double the time that machine B takes.
Let N = 2 items, A's time for N items = 2 days, and B's time for N items = 1 day.
Since A takes 2 days to produce 2 items, A's rate = w/t = 2/2 = 1 item per day.
Since B takes 1 day to produce 2 items, B's rate = w/t = 2/1 = 2 items per day.
Combined rate for A and B together = 1+2 = 3 items per day.
Working together at their respective rates, A and B can produce x items in 3 days.
In 3 days, the work produced by A and B together = (combined rate for A and B)(3 days) = 3*3 = 9 items.
Thus, x = 9.
How many days will it take machine A to produce x items?
Since A's rate alone = 1 unit per day, the time for A alone to produce 9 items = w/r = 9/1 = 9 days.
The correct answer is
C.
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