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# Working alone at its constant rate, machine K took 3 hours to produce

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Manager
Joined: 14 Jun 2008
Posts: 162
Working alone at its constant rate, machine K took 3 hours to produce [#permalink]

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26 Jul 2008, 09:32
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78% (01:48) correct 22% (01:30) wrong based on 579 sessions

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Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?

A. 8
B. 12
C. 16
D. 24
E. 30
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink]

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18 Jul 2011, 22:28
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1
sset009 wrote:
8. Working alone at its constant rate, machine K took 3 hours to produce ¼ of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the unites produced last Friday. How many hours would it have taken machine M, working along at its constant rate, to produce all of the units produced last Friday?
(A) 8
(B) 12
(C) 16
(D) 24
(E) 30

Try using Ratios. It needs some effort in the beginning but is very rewarding. I solve all these questions orally using ratios. I will tell you how.

Working alone at its constant rate, machine K took 3 hours to produce ¼ of the units produced last Friday.

Ok. K takes 3 hrs for 1/4 of units so it takes 12 hrs for all units.

Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the unites produced last Friday.

In 6 hrs, they both together produced 3/4 of units. K alone would have taken 9 hrs to produce 3/4 of units (since it takes 3 hrs for 1/4 of units)
Ratio of time taken together : time taken by K = 6:9 = 2:3
Ratio of speed together : speed of K = 3:2
Since speed together is 3 and speed of K is 2, speed of M alone is 1 i.e. speed of K is twice the speed of M. So M will take twice the time taken by K. Since K takes 12 hrs to produce all the units alone, M will take 24 hrs to produce all the units alone.

For more on Ratios, check

http://www.veritasprep.com/blog/2011/03 ... of-ratios/
http://www.veritasprep.com/blog/2011/03 ... os-in-tsd/
http://www.veritasprep.com/blog/2011/03 ... -problems/
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 16 Aug 2012 Posts: 3 Location: United States Schools: LBS '16, IE Nov'15 Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags Updated on: 30 Nov 2012, 03:07 3 9 Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday? A. 8 B. 12 C. 16 D. 24 E. 30 Originally posted by samdarsh88 on 29 Nov 2012, 22:44. Last edited by Bunuel on 30 Nov 2012, 03:07, edited 1 time in total. Renamed the topic, edited the question and added the OA. VP Joined: 02 Jul 2012 Posts: 1194 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 29 Nov 2012, 23:09 1 Lets assume the work to be something like moving 24 bricks. (Three fourths of 24 gives a multiple of 6 & one fourth of 24 gives a multiple of 3. Hence we are selecting 24 for ease of calculation. This method should work fine for any number) Machine K works at 2 bricks per hour K & M together work at 3 bricks per hour So, M works at 1 brick per hour So, M working alone would have took 24 hours. Answer should be D _________________ Did you find this post helpful?... Please let me know through the Kudos button. Thanks To The Almighty - My GMAT Debrief GMAT Reading Comprehension: 7 Most Common Passage Types Intern Joined: 16 Aug 2012 Posts: 3 Location: United States Schools: LBS '16, IE Nov'15 Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 30 Nov 2012, 00:21 the explanation sounds logical and the correct answer to this is D.Though,that's the (pick an answer an work upon) approach.how can we approach the same question through the conventional method (conceptual), by taking out the respective rates etc.can any one explain? Senior Manager Joined: 22 Dec 2011 Posts: 271 Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 30 Nov 2012, 00:32 7 samdarsh88 wrote: the explanation sounds logical and the correct answer to this is D.Though,that's the (pick an answer an work upon) approach.how can we approach the same question through the conventional method (conceptual), by taking out the respective rates etc.can any one explain? 1st 2nd and 3 columns are Rate, Time and Work done. R * 3 = 1/4 so rate of K = 1/12 Now 3/4 of the job is done by both K and M in 6 hrs (1/12 + rate of M ) * 6 = 3/4 solving we get rate of M = 1/24 Finally R * t = W 1/24 * t = 1 there t = 24 hrs HTH. Cheers Intern Joined: 16 Aug 2012 Posts: 3 Location: United States Schools: LBS '16, IE Nov'15 Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 30 Nov 2012, 00:41 thanks for the explanation jp27.seems ,i was committing a careless mistake before. Hail guys. VP Joined: 02 Jul 2012 Posts: 1194 Location: India Concentration: Strategy GMAT 1: 740 Q49 V42 GPA: 3.8 WE: Engineering (Energy and Utilities) Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 30 Nov 2012, 01:31 samdarsh88 wrote: the explanation sounds logical and the correct answer to this is D.Though,that's the (pick an answer an work upon) approach.how can we approach the same question through the conventional method (conceptual), by taking out the respective rates etc.can any one explain? As I mentioned in my previous comment, I was not picking an answer. Rather I was just picking a smart number. In this case both happened to be the same. The same method would work just as well with any other number. Illustration : Lets assume the work to be making 30 bricks : $$Rate of Machine K = \frac{30}{4*3} = \frac{30}{12}$$ $$Rate of K & M together = \frac{30*3}{4*6} = \frac{90}{24} = \frac{45}{12}$$ $$Rate of machine M = \frac{45}{12} - \frac{30}{12} = \frac{15}{12} = \frac{5}{4}$$ $$Machine M alone = \frac{30}{5/4} = \frac{120}{5} = 24$$ So, we can see that answer is still 24. I had picked 24 only to avoid fractions. _________________ Did you find this post helpful?... Please let me know through the Kudos button. Thanks To The Almighty - My GMAT Debrief GMAT Reading Comprehension: 7 Most Common Passage Types Manager Joined: 26 Jul 2011 Posts: 108 Location: India WE: Marketing (Manufacturing) Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 30 Nov 2012, 02:28 rate of machine k = (1/4)/3 (i.e it takes 3 hours to complete 1/4 of the work) ----> 1/12 Now both M and K working together at their respective rate complete 3/4 (the remaining work i.e 1- 1/4) of the work in 6 hours. 1/12 + 1/M = (3/4)/6 ------M = 24 hence the answer is D... Math Expert Joined: 02 Sep 2009 Posts: 46291 Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 30 Nov 2012, 03:18 4 1 samdarsh88 wrote: Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday? A. 8 B. 12 C. 16 D. 24 E. 30 Given that machines M and K, working together, can produce 3/4 of units in 6 hours. Since also given that machine K can produce 1/4 of units in 3 hours, then in 6 hours it can produce 2/4 of units. Which means that when working together, machine M produced 3/4-2/4=1/4 of units in 6 hours, thus it needs 6*4=24 hours to produce all of the units. Answer: D. _________________ Current Student Joined: 02 Jun 2015 Posts: 86 Location: Brazil Concentration: Entrepreneurship, General Management GPA: 3.3 Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 21 Dec 2015, 16:44 samdarsh88 wrote: Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday? A. 8 B. 12 C. 16 D. 24 E. 30 Machine K in 6 hours produced 2/4 As Machine K already had produced 1/4, so machine M produced only 1/4 in 6 hours 1/4x = 6 x = 24 SVP Joined: 08 Jul 2010 Posts: 2115 Location: India GMAT: INSIGHT WE: Education (Education) Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 09 Sep 2017, 19:03 sset009 wrote: Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday? A. 8 B. 12 C. 16 D. 24 E. 30 Answer: option D Check attachment Attachments File comment: www.GMATinsight.com Sol 2.jpg [ 97.95 KiB | Viewed 2490 times ] _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html 22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 11815 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink] ### Show Tags 03 Mar 2018, 15:37 Hi All, As wordy and complex as this question might first appear, you can break it down into pieces and solve with very little in the way of tough calculations. We're told that Machine K took 3 hours to produce 1/4 of the units. From this, we have a rate (every 3 hours another 1/4 of the units are produced). Machines K and M took 6 more hours to finish producing the rest of the units. Let's break this into two pieces: Machine K worked for 6 more hours Machine M worked for 6 hours We know Machine K's rate: 3 hours to complete 1/4 of the units. Since it worked 6 more hours, Machine K completed 2(1/4) = 1/2 of the units during that time. Counting the initial 3 hours (and 1/4 of the units) that Machine K worked, it completed 1/4 + 1/2 = 3/4 of the units. The remaining 1/4 of the units must have been produced by Machine M over the course of those 6 hours…. Machine M takes 6 hours to produce 1/4 of the units. We're asked how long it would take Machine M to produce ALL of the units… 6 hours to produce 1/4 of the units = 24 hours to produce all of the units. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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VP
Joined: 07 Dec 2014
Posts: 1020
Working alone at its constant rate, machine K took 3 hours to produce [#permalink]

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03 Mar 2018, 18:33
sset009 wrote:
Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?

A. 8
B. 12
C. 16
D. 24
E. 30

if K can produce 2*1/4=1/2 of all units alone in 6 hours,
then M produces 3/4-1/2=1/4 of of all units when they work together for 6 hours
M can produce all the units in 4*6=24 hours
D
Intern
Joined: 15 Oct 2016
Posts: 31
Re: Working alone at its constant rate, machine K took 3 hours to produce [#permalink]

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03 Mar 2018, 23:24
sset009 wrote:
Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?

A. 8
B. 12
C. 16
D. 24
E. 30

Let's say there are 12 units of work to be done.

So, K does 1 unit of work per hour and completes 3 units of work alone.

Both machines together did 9 units of work in 6 hours => 1.5 units / hr => M does 0.5 units / hr

So to complete 12 units, all by itself, M would take 24 hours.
Re: Working alone at its constant rate, machine K took 3 hours to produce   [#permalink] 03 Mar 2018, 23:24
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