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A company has two types of machines, type R and type S

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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. 3
B. 4
C. 6
D. 9
E. 12
[Reveal] Spoiler: OA

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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


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 --> \(Time*Rate=2*\frac{1}{12}x=1=Job\) --> \(x=6\).

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

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After tearing my hair apart for 30 mins, saw Bunuels solution and realized the question is wrong. Its 18 not 8

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

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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
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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

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

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\(Let N be the number of machines...\)
\(\frac{N}{36}+\frac{N}{18}(2hours)=1\)
\(\frac{3N}{18}=1==>N=6\)

ANswer: 6 machines
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Re: A company has two types of machines, type R and type S [#permalink]

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New post 25 Feb 2013, 02:36
So the number of macines in this question is just the time in this particular question?
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Re: A company has two types of machines, type R and type S [#permalink]

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New post 25 Feb 2013, 13:29
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?

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

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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


2x/36 + 2x/18 = 1

x = 6

C

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

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New post 25 Nov 2014, 13:51
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?

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mns18051985 wrote:
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.
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Re: A company has two types of machines, type R and type S [#permalink]

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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

So, x/36 +x/18 =1/2
x3/36=1/2
x=36/6=6

So no of machine R is 6

Answer C

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

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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.

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

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New post 10 Jan 2015, 11:23
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...

Shouldn't the answer be E)12

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

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New post 11 Jan 2015, 10:47
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.
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Re: A company has two types of machines, type R and type S [#permalink]

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New post 11 Jan 2015, 10:58
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.



Clear...... simple... thanks a ton. :)

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

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New post 25 Nov 2015, 21:31
X = number of machines
1/36+2/36 = 1job
(3/36)*2X = 1job
6x/36 =1job
X=6

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

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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.

Therefore, x+2x = 18, 3x = 18, x=6. [Correct Answer]

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

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New post 03 Nov 2016, 20:54
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

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

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New post 04 Nov 2016, 15:05
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


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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Re: A company has two types of machines, type R and type S   [#permalink] 04 Nov 2016, 15:05

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