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Guest
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Post subject: A company has two types of machines, type R and type S  Posted: Sat Nov 10, 2007 10:24 am |
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Could please somebody explain solution of the problem?
A company has two types of machines, type R and type S. Operating as a constant rate, a machine 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 machines 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
The correct answer is C. 6.
Thanks!
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Amit
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Post subject: Re: A company has two types of machines, type R and type S Posted: Sun Nov 11, 2007 8:44 pm |
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Guest wrote: Could please somebody explain solution of the problem?
A company has two types of machines, type R and type S. Operating as a constant rate, a machine 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 machines 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
The correct answer is C. 6.
Thanks!
Machine R can do 1 job / 36hrs. S does 1 job / 18 hrs. We want the total to be 1 job / 2hrs
So this is the equation where x represents the number of machines you need:
rate of R + rate of S = rate of total
x/36 + x/18 = 1/2
(multiply all by 36)
x + 2x = 18
3x = 18
x = 6 machines
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RonPurewal
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Post subject: Posted: Fri Nov 16, 2007 6:47 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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That's it.
There are some ways to streamline this problem - such as using a 'rate chart' with (work rate) x (time) = (total work done) - but the essence of the problem will still be exactly what's here.
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Guest
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Post subject: Posted: Wed Nov 21, 2007 7:26 pm |
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I have it is saying how many type of R machine used. I presume 6 means ( same no. of S + same no. of R)
so total number of R machine should be 3. Please correct if I am wrong
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Guest
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Post subject: Posted: Wed Nov 21, 2007 8:12 pm |
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Let me correct I post wrong 3 Answer is 6
It is like this
In 12 hours R + S can finish a job
so in 1 hours the set finish 1/12 of the work
in 2hours the set (R + S) finish 1/6 of the work
so inorder to finish full work we need 6 sets of (R+S).
Hence R machine needed R=6
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RonPurewal
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Post subject: Posted: Thu Nov 22, 2007 3:47 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Yep - if you look at the setup of the algebra done earlier in the post, you'll notice that the equation includes 'x' of machine R *AND* 'x' of machine S.
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Guest
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Post subject: Posted: Tue Nov 27, 2007 12:39 pm |
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When I set this problem up I had it like this: x/36 + y/18 = 1/2. Where x and y where the number of each type of machine.
If the company used the same number of machines to do the job in 2 hours, how many machines of type R were used?
Where it says same number of machines, can that be interpreted as the same number of machine r as the number of machine s?
Kind of crucial wording that totally screwed me up.[/b][/i]
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RonPurewal
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Post subject: Posted: Fri Nov 30, 2007 5:16 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Anonymous wrote: Where it says same number of machines, can that be interpreted as the same number of machine r as the number of machine s?
I'm assuming that was a typo - a 'streamlined' version of the original question that obfuscates its original meaning. Interestingly, I didn't even notice that when I responded to this thread earlier.
Moreover, that's what the problem has to mean; otherwise, there are many combinations of machines that will solve the problem, as machine S is exactly twice as fast as machine R: we could just take away one machine S and replace it with two R's (or vice versa), and the new combination would also work. Since this isn't data sufficiency (i.e., we need a UNIQUE solution), that won't do.
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Guest
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Post subject: Posted: Sun Jun 15, 2008 6:44 pm |
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------------1 machines-----1 machines
Rate-----------Rr---------------Sr----------
Time --------36----------------18---------(hrs)
Work--------1 job-----------1 job
W=rt
1*36*Rr=1*18*Sr
Sr=2*Rr
------------x machines-----x machines -----(Same machines)
Rate-----------Rr---------------Sr----------
Time --------2----------------2---------(hrs)
Work--------1 job-----Total work done by both machines
Work=2*Rr*x+2*Sr*x
=2x(Rr+Sr)
=2x(3Rr) ---Since Sr=2Rr
=6xRr
6xRr=36Rr ---job done by Rr from step 1
x=6
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mathmaster
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Post subject: R&S Posted: Wed Jun 18, 2008 4:11 am |
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assume the task is to lay bricks so R - 1 brick per hour =36 hours : s 2 bricks per hour = 18 hours the ratio is 2:1
hence inorder to do the job in 2 hours need to lay 18 bvricks per hour in the ratio 1:2 hence the answer is 6
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RonPurewal
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Post subject: Posted: Wed Jun 18, 2008 5:19 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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nice wealth of solutions to this problem.
sweetness
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Guest
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Post subject: Posted: Mon Aug 04, 2008 1:21 pm |
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m seein complex solutions here :)
in one hour machine a does 1/36 B does 1/ 18
one hour combined 1/36 + 1/18 = 1/12 ----> 1 hour
2 hours amount of wok done = 2/12 == 1/ 6
since num of machines is the same it shud be 6 .....
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RonPurewal
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Post subject: Posted: Wed Aug 13, 2008 3:37 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Anonymous wrote: m seein complex solutions here :)
in one hour machine a does 1/36 B does 1/ 18
one hour combined 1/36 + 1/18 = 1/12 ----> 1 hour
2 hours amount of wok done = 2/12 == 1/ 6
since num of machines is the same it shud be 6 .....
this is a nice compact solution.
next time, please write out words in full, so that your posts are easier to read. thank you.
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alexei600
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Post subject: Re: A company has two types of machines, type R and type S Posted: Wed Feb 09, 2011 1:48 pm |
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| Course Students |
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Posts: 34
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Instr.
When I do (1/36+1/18)*2=1/6
Combined rates of each mach. respect. mult. 2 hours. How can I derive from 1/6 , 6 machines?
Thanks
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RonPurewal
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Post subject: Re: A company has two types of machines, type R and type S Posted: Fri Feb 11, 2011 6:12 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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alexei600 wrote: Combined rates of each mach. respect. mult. 2 hours. i don't know what this is supposed to say; please re-type your post in complete sentences, with words that are not abbreviated. thanks much.
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