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?
(x - y)/(x + y)
x/(y - x)
(x + y)/xy
y/(x - y)
y/(x + y)
Let the job = 10 units.
Let x = 5 hours.
Rate for A alone = w/t = 10/5 = 2 units per hour.
Let y = 2 hours.
Rate for B alone = w/t = 10/2 = 5 units per hour.
The combined rate for A+B = 2+5 = 7 units per hour.
Of the 7 units produced each hour, 2 will produced by A and 5 will be produced by B.
Thus, the fraction of the job produced by A = 2/7. This is our target.
Now we plug x=5 and y=2 into the answers to see which yields our target of 2/7.
A quick scan of the answers reveals that only
E works:
y/(x+y) = 2/(5+2) = 2/7.
The correct answer is
E.
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