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
Answer e
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Combined rate, difficult without plugging values?
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Anju@Gurome
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Fraction of the job that B will not have to complete = Fraction of the job that A will completeclaudayst 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?
Algebraic Approach:
In 1 hour, A completes 1/x of the job.
In 1 hour, B completes 1/y of the job.
In 1 hour, A and B together complete (1/x + 1/y) = (x + y)/xy of the job.
Hence, A and B together will complete the job in xy/(x + y) hours.
In xy/(x + y) hours A will do [xy/(x + y)]*(1/x) = y/(x + y) of the job.
The correct answer is E.
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Tricky Approach:
Let us assume that A completes the job in zero hours, i.e. A completes the job alone and we don't need B to do any part of the job. (This is practically impossible but mathematics should hold for this situation also)
Hence, x = 0
We will put this value of x in the given options to see which of them is equal to 1.
Let us assume that A completes the job in zero hours, i.e. A completes the job alone and we don't need B to do any part of the job. (This is practically impossible but mathematics should hold for this situation also)
Hence, x = 0
We will put this value of x in the given options to see which of them is equal to 1.
- A. (x - y)/(x + y) = -y/y = -1 --> NO
B. x/(x + y) = 0 --> NO
C. (x + y)/(xy) = Not definite --> NO
D. y/(x - y) = -y/y = -1 --> NO
E. y/(x + y) = y/y = 1 --> YES
Anju Agarwal
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In other words:claudayst 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?
(x - y)/(x + y)
x/(y - x)
(x + y)/xy
y/(x - y)
y/(x + y)
What fraction of the job will be completed by A?
The TIME RATIO for A and B = x:y.
Since time and rate are reciprocals, the RATE RATIO for A and B = y : x.
Implication of the rate ratio:
Of every y+x units produced each hour, A produces y units and B produces x units.
Thus, (work produced by A each hour)/(total work produced each hour) = y/(y+x).
The correct answer is E.
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As a tutor, I don't simply teach you how I would approach problems.
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