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

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

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04 Nov 2016, 15:05
1
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

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Work/Rate problem- A company has..  [#permalink]

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01 Jan 2017, 06:10
A company has two types of machines, Type R and Type S. Operating at a certain 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 uses the same number of each type of machine to do the job in 2 hours, how many machines of Type R were used?

Options:
A. 3
B. 4
C. 6
D. 9
E. 12

Can anybody give me a quickest and simpler way to solve this? I took almost 3.5 min on this question to solve during a mock test. Still ended up guessing as I wasn't sure of the approach.
Thanks.
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Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: Work/Rate problem- A company has..  [#permalink]

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01 Jan 2017, 06:47
5
1
baalok88 wrote:
A company has two types of machines, Type R and Type S. Operating at a certain 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 uses the same number of each type of machine to do the job in 2 hours, how many machines of Type R were used?

Options:
A. 3
B. 4
C. 6
D. 9
E. 12

Can anybody give me a quickest and simpler way to solve this? I took almost 3.5 min on this question to solve during a mock test. Still ended up guessing as I wasn't sure of the approach.
Thanks.

We are given rates of each machine and that the number of machines of each type being used is the same = x.

$$\frac{x}{36} + \frac{x}{18} = \frac{1}{2}$$

$$\frac{3x}{36} = \frac{1}{2}$$

$$6x = 36$$

$$x = 6$$
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Posts: 23
Re: A company has two types of machines, type R and type S  [#permalink]

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07 Jan 2017, 21:07
2
Rate(R) = $$\frac{1}{36}$$
Rate(S) = $$\frac{1}{18}$$
Combined rate of both machines ,
Rate(RS)=Rate(R) + Rate(S) = $$\frac{1}{12}$$

we have given time , T = 2hrs , Workdone = 1 (for single job)
Plug in the values :

[Rate] * [Time] * [No. of machines] = Workdone

$$\frac{1}{12}$$ * 2 * [No. of machines] = 1
[No. of machines] = 6

Ans : C
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Joined: 29 Nov 2016
Posts: 9
Re: A company has two types of machines, type R and type S  [#permalink]

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18 Apr 2017, 05:05
Bunuel wrote:
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 --> $$Time*Rate=2*\frac{1}{12}x=1=Job$$ --> $$x=6$$.

When I am double checking, why am I not getting the right answer?
If 1 R machine is taking 36 hours, then 6 R machines will take 6 hours.
If 1 S machine is taking 18 hours, then 6 S machines will take 3 hours.
Together, they will take 6-3=3 hours.

Please tell me where am I wrong :/
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Joined: 14 May 2017
Posts: 47
Re: A company has two types of machines, type R and type S  [#permalink]

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16 Aug 2017, 18:41
narendran1990 wrote:
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]

I was trying to solve using similar kind of method. But i could not understand how you arrived on 18? It will be great if you could elaborate.
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GPA: 3.4
A company has two types of machines, type R and type S  [#permalink]

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09 Nov 2017, 21:26
There is no need to compute the combined rate in this case, explicitly that is.

Since the number of machines is the same, we can use a simple equation:

$$x*\frac{1}{36}+ x* \frac{1}{18} = \frac{1}{2}$$ (here x machines work at the respective rates for 2 hours)

Solving for x, we get 6.
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Re: A company has two types of machines, type R and type S  [#permalink]

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13 Nov 2018, 19:46
hannahkagalwala wrote:
Bunuel wrote:
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 --> $$Time*Rate=2*\frac{1}{12}x=1=Job$$ --> $$x=6$$.

When I am double checking, why am I not getting the right answer?
If 1 R machine is taking 36 hours, then 6 R machines will take 6 hours.
If 1 S machine is taking 18 hours, then 6 S machines will take 3 hours.
Together, they will take 6-3=3 hours.

Please tell me where am I wrong :/

It is not correct to subtracting time taken by one machine from that of other to calculate final time,

Time taken are for complete job, and if other machines are also performing the same job, then there will be less amount of work of each machine type and hence leaser time will be taken.

You are right till, 6 R machines will take 6 hours.
And 6 S machines will take 3 hours.

Now total time taken will be 1/(1/6 +1/3) = 1/(1/2) = 2 hours.

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Re: A company has two types of machines, type R and type S &nbs [#permalink] 13 Nov 2018, 19:46

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