In a Factory, three machines \(A, B\) and \(C,\) Working at the same time and at their respective constant rate can do

[Vincen]

In a Factory, three machines \(A, B\) and \(C,\) Working at the same time and at their respective constant rate can do a job in \(8\) hours, \(A\) and \(B\) working at their constant rate can do the same job in \(12\) hours. How many hours would it take \(C,\) working alone at its constant rate, to do the same job?

A) 20

B) 22

C) 24

D) 16

E) 32

Answer: C

Source: e-GMAT

[Scott@TargetTestPrep]

In a Factory, three machines \(A, B\) and \(C,\) Working at the same time and at their respective constant rate can do a job in \(8\) hours, \(A\) and \(B\) working at their constant rate can do the same job in \(12\) hours. How many hours would it take \(C,\) working alone at its constant rate, to do the same job?

A) 20

B) 22

C) 24

D) 16

E) 32

Answer: C

Solution:

Let a, b, and c be the number of hours A, B, and C can finish the job by itself alone, respectively. Then their rates are 1/a, 1/b, and 1/c, respectively. We can create the equations (notice that we need to determine the value of c):

1/a + 1/b + 1/c = 1/8

and

1/a + 1/b = 1/12

Subtracting the second equation from the first, we have:

1/c = 1/8 - 1/12

1/c = 3/24 - 2/24

1/c = 1/24

c = 24

Answer: C