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Machine A, machine B, and machine C, working together at their respect

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Machine A, machine B, and machine C, working together at their respect  [#permalink]

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New post 09 May 2018, 11:05
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Question Stats:

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Machine A, machine B, and machine C, working together at their respective constant rates, can complete a certain job in 24 hours. How many hours would it take machine A, working alone at its constant rate, to complete the same job?


(1) Machines B and C, working together at their respective constant rates, can complete the job in 36 hours.

(2) Machines A and C, working together at their respective constant rates, can complete the job in 48 hours.

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Re: Machine A, machine B, and machine C, working together at their respect  [#permalink]

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New post 09 May 2018, 14:15
Bunuel wrote:
Machine A, machine B, and machine C, working together at their respective constant rates, can complete a certain job in 24 hours. How many hours would it take machine A, working alone at its constant rate, to complete the same job?


(1) Machines B and C, working together at their respective constant rates, can complete the job in 36 hours.

(2) Machines A and C, working together at their respective constant rates, can complete the job in 48 hours.


To help avoid confusion, we'll first translate our question into equations, which will help us see what we need to do.
This is a Precise approach.

Our stem gives 24*(a + b + c) = j where a,b,c are the rates of A,B,C respectively, and j is the given job.
We need to solve for t (=time) such that a*t=j

(1) 36*(b+c)=j
So if 24(a+b+c)=36(b+c) then 24a = 12(b+c) so 2a = b+c. Substituting into 24(a+b+c)=j lets us solve the question.
Sufficient!

(2) 48*(a+c)=j
So we can write 24(a+b+c)=48(a+c) which gives 24a = 24b - 24c so a = b - c.
So our two equations are a = b - c and 24(a+b+c)=j. We have no way to combine these two equation to solve the question.
Insufficient.

(A) is our answer.
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Re: Machine A, machine B, and machine C, working together at their respect  [#permalink]

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New post 11 Apr 2019, 11:38
Bunuel wrote:
Machine A, machine B, and machine C, working together at their respective constant rates, can complete a certain job in 24 hours. How many hours would it take machine A, working alone at its constant rate, to complete the same job?


(1) Machines B and C, working together at their respective constant rates, can complete the job in 36 hours.

(2) Machines A and C, working together at their respective constant rates, can complete the job in 48 hours.



given
1/a+1/b+1/c=1/24
a+b+c/abc = 1/24

#1
1/b+1/c = 1/36

so we can find 1/a = 1/24-1/36 ; a = 72 hrs
sufficient
#2
1/a +1/c= 1/48
not sufficient as 1/c not given
IMO A
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Re: Machine A, machine B, and machine C, working together at their respect   [#permalink] 11 Apr 2019, 11:38
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