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Work Problem - Machine R and S

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Work Problem - Machine R and S

by actofman » Tue Apr 23, 2013 12:58 am
Another question here.

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to the job in 2 hours, how many machines of type R were used?
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by Anju@Gurome » Tue Apr 23, 2013 1:09 am
actofman wrote:A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type of machine to the job in 2 hours, how many machines of type R were used?
In 1 hour,
  • One machine of type R does 1/36th of the job
    One machine of type S does 1/18th of the job
    One machine of type R and One machine of type S together does (1/36 + 1/18) = 3/36 = 1/12th of the job
So, one machine of type R and one machine of type S R and S together take 12 hours to finish the job.

Now if the job is to be done in 2 hours, we'll need 12/2 = 6 machines of each type
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by GMATGuruNY » Tue Apr 23, 2013 1:36 am
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hours and a machine of type S does the same job in 18 hours. If the company used the same number of each type
of machine to do the job in 2 hours, how many machines of type R were used ?

A) 3
B) 4
C) 6
D) 9
E) 12
Let the job = 36 units.
Rate for machine R = 36/36 = 1 unit per hour.
Rate for machine S = 36/18 = 2 units per hour.
Combined rate for R+S = 1+2 = 3 units per hour.
To complete the job in 2 hours, the number of units that must be produced each hour = 36/2 = 18 units.
Since using one of each machine will produce 3 units per hour, and 18 total units must be produced, each hour the number of machines needed = w/r = 18/3 = 6.

The correct answer is C.
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