hey_thr67 wrote:Machine A can complete a certain job in x hours. Machine B can complete the same job in y hours. If A and B work together at their respective rates to complete the job, which of the following represents the fraction of the job that B will not have to complete?
A:
x - y
------
x + y
B:
x
-----
y - x
C:
x + y
-----
xy
D:
y
-----
x - y
E:
y
----
x + y
OA is E
Time and rate are RECIPROCALS.
Let x = 2 hours and y = 5 hours.
Since the ratio of A's time to B's time = 2:5, the ratio of A's rate to B's rate = 5:2.
The ratio of the rates implies the following:
Of every 7 units produced, 5 will be produced by A and 2 will be produced by B, implying that the fraction not produced by B = 5/7. This is our target.
Now we plug x=2 and y=5 into the answers to which yields our target of 5/7.
A quick scan of the answer choices reveals that only
E works:
y/(x+y) = 5/(2+5) = 5/7.
The correct answer is
E.
Note that the same reasoning can be applied directly to the variables themselves.
Since the ratio of A's time to B's time = x:y, the ratio of A's rate to B's rate = y : x.
The ratio of the rates implies the following:
Of every (x+y) units produced, y will be produced by A, implying that the fraction not produced by B = y/(x+y).
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