## 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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### Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job.

by BTGmoderatorDC » Sun Jun 28, 2020 6:08 pm
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

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### Re: Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same

by [email protected] » Tue Jun 30, 2020 12:06 am
BTGmoderatorDC wrote:
Sun Jun 28, 2020 6:08 pm
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
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.

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

Hope this helps!

-Jay
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### Re: Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same

by [email protected] » Mon Apr 19, 2021 6:19 am
BTGmoderatorDC wrote:
Sun Jun 28, 2020 6:08 pm
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

Solution:

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.