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work problem

by grandh01 » Thu Jul 12, 2012 11:01 pm
A company has 2 types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hrs. If the company used the same number of each type of machine to do the job in 2 hrs, how many machines of type R were used?

1)3
2)4
3)6
4)9
5)12

Thanks in advance
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by Anurag@Gurome » Thu Jul 12, 2012 11:11 pm
grandh01 wrote:A company has 2 types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hrs. If the company used the same number of each type of machine to do the job in 2 hrs, how many machines of type R were used?
Say, the company has used n type R machines and n type S machines.
Now a single type R machine does 1/36 of the job in one hour and a type machine does 1/18 of the job in one hour.

Hence, in one hour one type R and one type S machine together do (1/36 + 1/18) = 3/36 = 1/12 of the job

In 2 hours, n type R and n type S machine together do 2*n*(1/12) = n/6 of the job

We know, n/6 = 1 --> n = 6

The correct answer is C.
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by GMATGuruNY » Sat Jul 14, 2012 2:34 am
grandh01 wrote:A company has 2 types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hrs. If the company used the same number of each type of machine to do the job in 2 hrs, how many machines of type R were used?

1)3
2)4
3)6
4)9
5)12

Thanks in advance

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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