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A company has two types of machines, type R and type S [#permalink]

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02 Apr 2012, 13:55

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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 hrs 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 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 hrs 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

Rate of A - \(\frac{1}{36}\) job/hour, rate of x machines of A - \(\frac{1}{36}x\) job/hour; Rate of B - \(\frac{1}{18}\) job/hour, rate of x machines of B - \(\frac{1}{18}x\) job/hour, (same number of each type);

Remember that we can sum the rates, hence combined rate of A and B is \(\frac{1}{36}x+\frac{1}{18}x=\frac{3}{36}x=\frac{1}{12}x\) job/hour.

We are told that together equal number (x in our case) of machines A and B can do the job (1 job) in 2 hours --> \(Time*Rate=2*\frac{1}{12}x=1=Job\) --> \(x=6\).

Re: A company has two types of machines, type R and type S [#permalink]

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03 Apr 2012, 06:49

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enigma123 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 hrs 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

Take total work as 360

R: work : 360 time: 36hrs rate: 10(calculaed)

S: Work:360 time 18hrs rate: 20( calculated)

together

given work:360 time2 hrs calculated: 180 rate: 180/(10+20) = 180/30 = 6 each
_________________

Regards, Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

A company has two types of machines, type R and type S [#permalink]

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15 Aug 2012, 11:16

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above720 wrote:

Here is a work problem from GMATPrep, Practice Test 1:

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 in 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

Machine R does a job in 36 Hours. Machine S in 18 Hours. Together, the machines R & S can finish the job in \(\frac{(36*18)}{(36+18)}= 12 Hours\) In other words, 1 machine of R + 1 machine of S can finish the job together in = 12 Hours

So, to finish the job in 2 Hours, company needs 6 machines of each type - Option C

Re: A company has two types of machines, type R and type S [#permalink]

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25 Feb 2013, 14:29

I am not sure I understand your question correctly. The number of machines is not equal to the time. Instead, the number of machines has to be replied with the time taken by each machine to get the total time required to complete the job.

Hope this helps but in case it doesn't, could you please state your question more elaborately?

fozzzy wrote:

So the number of macines in this question is just the time in this particular question?

Re: A company has two types of machines, type R and type S [#permalink]

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10 Jan 2014, 10:24

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enigma123 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 hrs 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?

Re: A company has two types of machines, type R and type S [#permalink]

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25 Nov 2014, 14:51

Could someone please clarify why the answer is not 3 each? I understand how to get to 6 machines and do it quickly but why isn't this 6 machines total since it is a combined rate?

Could someone please clarify why the answer is not 3 each? I understand how to get to 6 machines and do it quickly but why isn't this 6 machines total since it is a combined rate?

x in the solution HERE is the number of type R machines as well as the number of type S machines (we are told that the company used the same number of each type of machine to do the job ). So, when we solve for x, we get what we want.
_________________

Re: A company has two types of machines, type R and type S [#permalink]

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26 Nov 2014, 06:01

Rate of machine R =1/36 Rate of machine S =1/18

since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x

Re: A company has two types of machines, type R and type S [#permalink]

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26 Nov 2014, 21:30

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R finishes job in 36h and S does the same in 18h. So if both work together, the job will be done in 12h: 1/36 + 1/18 will give you 1/12. Now if one pair of R & S finishes job in 12h, how many such pairs are needed to finish the same job in 2h? 12/2 = 6 pairs of R & S. Hence 6 of R machines are required.

Re: A company has two types of machines, type R and type S [#permalink]

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10 Jan 2015, 12:23

Doubt....

1 machine A and 1 machine B together do 1/12 of the job in 1 hour.

We need to do 6/12 of the job in 1 hour... So 6 A machines and 6 B machines will be needed for 6/12 job in 1 hour... and 12 A and B machines will do 12/12 of the job in 2 hours...

1 machine A and 1 machine B together do 1/12 of the job in 1 hour.

We need to do 6/12 of the job in 1 hour... So 6 A machines and 6 B machines will be needed for 6/12 job in 1 hour... and 12 A and B machines will do 12/12 of the job in 2 hours...

Shouldn't the answer be E)12

6 A's and 6 B's do half of the job in 1 hour, so 6 A's and 6 B's will do the whole job in 2 hour and this is what we are asked to find.
_________________

Re: A company has two types of machines, type R and type S [#permalink]

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11 Jan 2015, 11:58

Bunuel wrote:

gmathopeful90 wrote:

Doubt....

1 machine A and 1 machine B together do 1/12 of the job in 1 hour.

We need to do 6/12 of the job in 1 hour... So 6 A machines and 6 B machines will be needed for 6/12 job in 1 hour... and 12 A and B machines will do 12/12 of the job in 2 hours...

Shouldn't the answer be E)12

6 A's and 6 B's do half of the job in 1 hour, so 6 A's and 6 B's will do the whole job in 2 hour and this is what we are asked to find.

Re: A company has two types of machines, type R and type S [#permalink]

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17 Sep 2016, 23:30

Took 36 as the unit of work to be completed by R & S. [LCM of 36 & 18].

So, R does 1 unit per hour & S does 2 units per hour. Since an equal number of R & S machines have to be deployed, consider 'x' as the number of equipment. Additionally, the work is to be completed in 2 hours, so 18 units have to be manufactured.

Re: A company has two types of machines, type R and type S [#permalink]

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03 Nov 2016, 21:54

yezz 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

I think answer should be A, where am i going wrong folks??

let x be the number of each type of machine. given R & S working together will complete the work in 12hrs i.e., x/36+x/18= 3x/36= x/12 you need to complete the work in 2 hrs so you will need more of both machines. the company used the same number of each type of machine to do the job in 2 hours condition now you know x/12 work is done in 1 hour if 1 each of R & S are used so if 6 of each type of machine will complete the work in 2 hrs

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 hrs 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

We have a combined worker problem for which we can use the following formula:

work (1 machine) + work (2 machine) = total work completed

Since we are completing one job, we can say:

work (1 machine) + work (2 machine) = 1

We are given that 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.

Thus, the rates for the two machines are as follows:

rate of machine R = 1/36

rate of machine S = 1/18

We are also given that the company used the same number of each type of machine to do the job in 2 hours. If we let x = the number of each machine used, we can multiply each rate by x and we have:

rate of x number of R machines = x/36

rate of x number of S machines = x/18

Finally, since we know some number of R and S machines worked for two hours, and since work = rate x time, we can calculate the work done by each type of machine.

work done by x number of R machines = 2x/36 = x/18

work done by x number of S machines = 2x/18 = x/9

Now we can determine x using the combined worker formula:

work (machine R) + work (machine S) = 1

x/18 + x/9 = 1

x/18 + 2x/18 = 1

3x/18 = 1

x/6 = 1

x = 6

Answer: C
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