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Buy "All-In-One Standard ($149)", get free Daily quiz (2 mon). Coupon code : SPECIAL # Machines A and B always operate independently and at their r  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 52917 Machines A and B always operate independently and at their r [#permalink] ### Show Tags 07 Mar 2014, 03:48 00:00 Difficulty: 5% (low) Question Stats: 89% (01:17) correct 11% (01:50) wrong based on 690 sessions ### HideShow timer Statistics The Official Guide For GMAT® Quantitative Review, 2ND Edition Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ? (A) 3 1/3 (B) 3 (C) 2 1/2 (D) 2 1/3 (E) 1 1/2 Problem Solving Question: 140 Category: Algebra Applied problems Page: 80 Difficulty: 600 GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution. We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation. Thank you! _________________ Math Expert Joined: 02 Sep 2009 Posts: 52917 Re: Machines A and B always operate independently and at their r [#permalink] ### Show Tags 07 Mar 2014, 03:48 SOLUTION Machines A and B always operate independently and at their respective constant rates. When working alone, Machine A can fill a production lot in 5 hours, and Machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x ? (A) 3 1/3 (B) 3 (C) 2 1/2 (D) 2 1/3 (E) 1 1/2 From the stem: 1/5 + 1/x = 1/2 --> x = 10/3. Answer: A. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8882 Location: Pune, India Machines A and B always operate independently and at their r [#permalink] ### Show Tags 07 Mar 2014, 04:24 3 Work Rate problems are based on the concept that rates are additive. That is to say that if I paint half a wall in an hour and if you paint half a wall in an hour, if we both work together on a wall, we will finish the wall in an hour (Assuming that you are not repainting whatever I am painting to cover up my shoddy work!). Remember, Rate of work = Work done per unit time So, the proper way to express rate is 1/2 wall per hour and not 1 wall in 2 hours If my rate of work is 1/2 wall/hour and yours is 1/2 wall/hour, our total rate of work is 1/2 + 1/2 = 1 wall/hour. The basic questions of work rate are of the following form: If A, working independently, completes a job in 10 hours and B, working independently, completes a job in 5 hours, how long will they take to complete the same job if they are working together? Since A completes a job in 10 hours, his rate of work is 1/10th of the job per hour. B's rate of work is 1/5th of the job per hour. Their combined rate of work would then be 1/10 + 1/5 = 3/10th of the job per hour. As we said before, Rate of work = Work done/Time so 3/10 = 1/T (because 1 job has to be done) or T = 10/3 hours. This implies that A and B will together take 3.33 hours to do the job. Note: Time taken when A and B work together will obviously be less than time taken by A or B when they are working independently. Coming back to your question (finally! I know!), if A takes 5 hours to fill a lot and B takes x hours, and together they fill it in 2 hours, what is x? Rate of work of A = 1/5th of the lot per hour Rate of work of B = 1/xth of the lot per hour Combined rate of work = 1/2 of the lot per hour 1/2 = 1/5 + 1/x x = 10/3 hours Note: Without solving, I know that E cannot be the answer since they both together take 2 hours to complete the work so one person alone can definitely not do the work in less than 2 hours. Time for a Teaser: A and B, working together, can finish a job in 10 days, B and C, working together, can finish the same job in 12 days and A and C, working together, can finish the same job in 15 days. If all three work together, how long will they take to finish the same job? _________________ Karishma Veritas Prep GMAT Instructor Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options > Manager Joined: 20 Dec 2013 Posts: 229 Location: India Re: Machines A and B always operate independently and at their r [#permalink] ### Show Tags 07 Mar 2014, 17:31 1 Option A. Let total units of work=10 A's rate=2 u/hr B's rate=10/x u/hr. Combined=10/(2+10/x)=2 Solving this equation we get x=10/3 or 3.33 Posted from my mobile device Senior Manager Status: Math is psycho-logical Joined: 07 Apr 2014 Posts: 415 Location: Netherlands GMAT Date: 02-11-2015 WE: Psychology and Counseling (Other) Re: Machines A and B always operate independently and at their respective [#permalink] ### Show Tags 15 Jan 2015, 13:34 As most of the times in such problems, I am creating the RTW chart: _______R_____T___W A_____1/5____5____1 B____3/10____x____1 Both___1/2____2___1 So, now let me explain: From the stem we know that A is doing the job (1 job) in 5 hours. For under T we add 5. From R*T=W, we get R=W/T, so in this case R=1/5. So, we add this under R. From the stem we know that both machines together are doing the job in 2 hours. We add 2 under T and 1/2 under R. Now, since we have the conbined time of both of the machines and the time of machine A we can find the time for machine B: 1/2 - 1/5 = 3 /10 or even easier 0.5 - 0.2 = 0.3, which is 3/10. We add 3/10 under R for machine B. Finally, we are asked to find x, which is the time machine B needs to complete the job. Using R*T=W --> (3/10)X=1 -->(3X)/10 = 1 --> 3X = 10 --> X = 10/3 --> X = 3+1/3. *an easy way to calculate the mixed number (mixed fraction) is like this: To turn 10/3 to a mixed number you are looking to find a number with which you can multiply the denominator, add sth to it and get the nominator. So, you will always have the same denominator: in this case 3. You are looking for a number lower than the nominator. You will multiply your denominator with this number and add sth to get 10 (your nominator). For example, you have 3 in this case in the denominator, multiply 3 by 3 and you get 9, add 1 and you get 10. You are done. The number you multiplied your denominator with goes to the left of the fraction and what you added goes to the nomintor. You now have 3 + 1/3. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13546 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Machines A and B always operate independently and at their respective [#permalink] ### Show Tags 15 Jan 2015, 21:12 1 Hi All, This prompt is an example of a "Work Formula" question. Any time a question involves two entities (people, machines, etc.) working on a task together and there are no "twists" to the question (someone stops working, someone shows up late to the job, etc.), you can use the Work Formula: (A)(B)/(A+B) where A and B are the "times" that it takes for each entity to finish the job on his/her/its own. Here, we're told: Machine A can do the job in 5 hours Machine B can do the job in X hours Working together, the two machines can do the job in 2 hours. Using the Work Formula, we have: (5)(X)/(5 + X) = 2 5X = 10 + 2X 3X = 10 X = 10/3 hours So, Machine B can do the job on its own in 10/3 = 3 1/3 hours. 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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Re: Machines A and B always operate independently and at their r  [#permalink]

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24 Jul 2015, 16:32
1
1
Hi All,

This prompt can also be solved by using the Work Formula:

Work = (A)(B)/(A+B) where A and B are the individual times that it takes to complete the 'job'

We're told that 2 machines can complete a task in 5 hours and X hours, respectively and working together will take 2 hours to complete the task. Working together, it would take them...

(5)(X)/(5+X) = 2 hours to complete the task

Using a bit of algebra, we can now solve for X...

5X = 10 + 2X
3X = 10
X = 10/3

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Re: Machines A and B always operate independently and at their respective  [#permalink]

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28 Mar 2018, 09:33
niheil wrote:
Machines A and B always operate independently and at their respective constant rates. When working alone, machine A can fill a production lot in 5 hours, and machine B can fill the same lot in x hours. When the two machines operate simultaneously to fill the production lot, it takes them 2 hours to complete the job. What is the value of x?

(A) $$3 \frac{1}{3}$$

(B) $$3$$

(C) $$2\frac{1}{2}$$

(D) $$2\frac{1}{3}$$

(E) $$1\frac{1}{2}$$

The rate of machine A is ⅕, and the rate of machine B is 1/x. Their combined rate is ½. Thus, we can create the equation:

1/5 + 1/x = 1/2

Multiplying by 10x, we have:

2x + 10 = 5x

10 = 3x

x = 10/3 = 3 1/3

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Re: Machines A and B always operate independently and at their r  [#permalink]

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05 Dec 2018, 19:08

Time for a Teaser: A and B, working together, can finish a job in 10 days, B and C, working together, can finish the same job in 12 days and A and C, working together, can finish the same job in 15 days. If all three work together, how long will they take to finish the same job?

Re: Machines A and B always operate independently and at their r   [#permalink] 05 Dec 2018, 19:08
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