Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to
complete the same job. If x = 4y, and x decreases by 85 % what is the time taken by A and B together
to complete the job in hours?
(A) 3y/8
(B) 2y/6
(C) y
(D) 6y/19
(E) 8y/3
OA A
Source: Manhattan Prep
Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job.
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So, we know that machine B currently takes y hours to complete the same job, and given that x = 4y, and x decreases by 85%, we know that machine A would take x = 15% of 4y = 0.6y hours to complete the same job.BTGmoderatorDC wrote: ↑Sun Jun 28, 2020 6:08 pmMachine A currently takes x hours to complete a certain job. Machine B currently takes y hours to
complete the same job. If x = 4y, and x decreases by 85 % what is the time taken by A and B together
to complete the job in hours?
(A) 3y/8
(B) 2y/6
(C) y
(D) 6y/19
(E) 8y/3
OA A
Source: Manhattan Prep
So, together, they would take reciprocal of (1/0.6y + 1/y) hours
Reciprocal of (1/0.6y + 1/y) = Reciprocal of (10/6y + 1/y) = 3y/8 hours
Correct answer: A
Hope this helps!
-Jay
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Solution:BTGmoderatorDC wrote: ↑Sun Jun 28, 2020 6:08 pmMachine A currently takes x hours to complete a certain job. Machine B currently takes y hours to
complete the same job. If x = 4y, and x decreases by 85 % what is the time taken by A and B together
to complete the job in hours?
(A) 3y/8
(B) 2y/6
(C) y
(D) 6y/19
(E) 8y/3
OA A
We can let the original value of x = 100; thus, y = 25, and the new value of x is 15. Therefore, the job will take 1/(1/15 + 1/25) = 1/(5/75 + 3/75) = 1/(8/75) = 75/8 hours to complete when the two machines work together. Notice that y = 25, so 75/8 = 3y/8.
Alternate Solution:
After x is decreased by 85%, machine A can do the job in 15x/100 = 3x/20 hours. Thus, in one hour, machine A can do 20/3x of the job and machine B can do 1/y of the job. Working together, 20/3x + 1/y of the job is done in one hour. Substituting x = 4y, we get:
20/3(4y) + 1/y
5/3y + 1/y
5/3y + 3/3y
8/3y
Since 8/3y of the job is done in one hour, it will take 1/(8/3y) = 3y/8 hours to complete the job.
Answer: A
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