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Machine R and S

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by GmatKiss » Fri Nov 04, 2011 3:41 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
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by user123321 » Fri Nov 04, 2011 3:54 am
GmatKiss 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 do the job in 2 hours, how many machines of type R were used ?

A) 3
B) 4
C) 6
D) 9
E) 12
R does 1/36 th fraction of 1 job in an hour
S does 1/18 th fraction of that job in an hour
Both will do 1/36+1/18 th of job = 1/12th of job in an hour
=> they will do 1/6th of job in two hours
so if they have 6 machines of each one they will do the entire job in two hours.

hence 6 machines of R are required
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by GMATGuruNY » Fri Nov 04, 2011 4:22 am
GmatKiss 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 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.
To complete the job in 2 hours, the number of units produced each hour = 36/2 = 18 units.
Since using one of each machine will produce 1+2 = 3 units per hour, and 18 units must be produced, we need 18/3 = 6 of each machine.

The correct answer is C.
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by Anurag@Gurome » Fri Nov 04, 2011 4:27 am
GmatKiss 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 do the job in 2 hours, how many machines of type R were used ?

A) 3
B) 4
C) 6
D) 9
E) 12
In 1 hour, machine R does 1/36th of the job

In 1 hour, machine S does 1/18th of the job

In 1 hour, machine R and S together does 1/36 + 1/18 = 3/36 = 1/12th of the job or R + S together take 12 hours to do 1 job.

Now if the job is to be done in 2 hours, then we'll need 12/2 = 6 machines each.

The correct answer is C.
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