Sep 22 08:00 PM PDT  11:00 PM PDT A Revolutionary OnDemand GRE Prep Course with Target Test Prep. Try for $1 Sep 23 04:00 PM PDT  06:00 PM PDT Join my MyGuru for Free GMAT Math Refresher is the best workshop to learn about the basics and the advanced strategies required to get a 700+ GMAT score. Sep 23 08:00 PM PDT  09:00 PM PDT Learn how to evaluate your profile, skills, and experiences to determine if, when, and where you should apply to graduate school. Sep 27 08:00 PM PDT  09:00 PM PDT Working in collaboration with examPAL we will provide you with a unique online learning experience which will help you reach that higher score. Start your free 7 day trial today.
Author 
Message 
TAGS:


Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
WE: Business Development (Energy and Utilities)
Followers: 171
Kudos [?]:
2915
[0], given: 394

Working together at their respective constant rates, robot A [#permalink]
06 Jul 2018, 16:20
Question Stats:
77% (02:12) correct
22% (02:22) wrong based on 53 sessions
Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is \(\frac{3}{5}\)that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones? (A) 15.75 (B) 18 (C) 18.75 (D) 27.5 (E) 30
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test




Active Member
Joined: 07 Jan 2018
Posts: 694
Followers: 11
Kudos [?]:
769
[2]
, given: 88

Re: Working together at their respective constant rates, robot A [#permalink]
07 Jul 2018, 19:10
2
This post received KUDOS
Let us assume, Machine B can do x work in 1 minor, Machine B can do \(6x\) work in \(6 min\) It follows that Machine A is only 3/5 efficient as machine A hence, Machine A can do \(\frac{18}{5} x work in 6 min.\) From question, \(\frac{18}{5} x + 6x = 88\) because working together the two machines can polish \(88 pounds\) of gemstone in \(6 min.\) solving for x we get \(x = \frac{440}{48}\) This is the pound of gemstone machine B can polish in 1 min.The amount of gemstone that machine A can polish in 1 min is \(\frac{440}{48} * \frac{3}{5}\) Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min. or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min or, Machine A can polish 165 pound of gemstone in \(\frac{240}{1320} * 165\) min = 30 min
_________________
This is my response to the question and may be incorrect. Feel free to rectify any mistakes Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos



Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
WE: Business Development (Energy and Utilities)
Followers: 171
Kudos [?]:
2915
[1]
, given: 394

Re: Working together at their respective constant rates, robot A [#permalink]
10 Jul 2018, 06:12
1
This post received KUDOS
ExplanationWhen rate problems involve multiple situations, it can help to set up an initial “skeleton” W= RT chart for the solution. That way, you can determine what data is needed and fill in that data as you find it. Since the question asks how long robot A will take alone, the chart will look like this: Attachment:
image1.jpg [ 26.04 KiB  Viewed 2954 times ]
Work is known and the question asks for time, so robot A’s rate is needed. Call the rates a and b. Now set up another chart representing what you know about the two robots working together. Attachment:
image1.jpg [ 50.99 KiB  Viewed 2953 times ]
Now, 6(a + b) = 88 and, from the question stem, robot A’s rate is \(\frac{3}{5}\) of B’s rate. This can be written as \(a = \frac{3}{5}b\). To solve for a, substitute for b: \(a = \frac{3}{5} b\) \(\frac{5}{3}a = b\) \(6(a+ \frac{5}{3}a) = 88\) \(6 \frac{8}{3} a = 88\) \(a = \frac{11}{2}\) So A’s rate is pounds per minute. Now just plug into the original chart: Attachment:
image1.jpg [ 28.05 KiB  Viewed 2954 times ]
The time robot A takes to polish 165 pounds of gems is \(165/\frac{11}{2} =\frac{330}{165} = 30\) minutes.
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test



Director
Joined: 22 Jun 2019
Posts: 517
Followers: 4
Kudos [?]:
104
[0], given: 161

Re: Working together at their respective constant rates, robot A [#permalink]
10 Jul 2019, 03:47
amorphous wrote: Let us assume,
Machine B can do x work in 1 min or, Machine B can do \(6x\) work in \(6 min\)
It follows that Machine A is only 3/5 efficient as machine A hence, Machine A can do \(\frac{18}{5} x work in 6 min.\)
From question,
\(\frac{18}{5} x + 6x = 88\) because working together the two machines can polish \(88 pounds\) of gemstone in \(6 min.\)
solving for x we get \(x = \frac{440}{48}\) This is the pound of gemstone machine B can polish in 1 min. The amount of gemstone that machine A can polish in 1 min is \(\frac{440}{48} * \frac{3}{5}\) Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min. or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min or, Machine A can polish 165 pound of gemstone in \(\frac{240}{1320} * 165\) min = 30 min What's the reason the changing the from here, Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min. to here or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min ??????
_________________
New to the GRE, and GRE CLUB Forum? GRE: All About GRE  Search GRE Specific Questions  Download Vault Posting Rules: QUANTITATIVE  VERBAL
Questions' Banks and Collection: ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation.  ETS All Official Guides 3rd Party Resource's: All In One Resource's  All Quant Questions Collection  All Verbal Questions Collection  Manhattan 5lb All Questions Collection Books: All GRE Best Books Scores: Average GRE Score Required By Universities in the USA Tests: All Free & Paid Practice Tests  GRE Prep Club Tests Extra: Permutations, and Combination Vocab: GRE Vocabulary Facebook GRE Prep Group: Click here to join FB GRE Prep Group



Active Member
Joined: 07 Jan 2018
Posts: 694
Followers: 11
Kudos [?]:
769
[1]
, given: 88

Re: Working together at their respective constant rates, robot A [#permalink]
10 Jul 2019, 05:55
1
This post received KUDOS
huda wrote: amorphous wrote: Let us assume,
Machine B can do x work in 1 min or, Machine B can do \(6x\) work in \(6 min\)
It follows that Machine A is only 3/5 efficient as machine A hence, Machine A can do \(\frac{18}{5} x work in 6 min.\)
From question,
\(\frac{18}{5} x + 6x = 88\) because working together the two machines can polish \(88 pounds\) of gemstone in \(6 min.\)
solving for x we get \(x = \frac{440}{48}\) This is the pound of gemstone machine B can polish in 1 min. The amount of gemstone that machine A can polish in 1 min is \(\frac{440}{48} * \frac{3}{5}\) Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min. or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min or, Machine A can polish 165 pound of gemstone in \(\frac{240}{1320} * 165\) min = 30 min What's the reason the changing the from here, Hence, machine A can polish \(\frac{1320}{240}\) pound of gemstone in 1 min. to here or, Machine A can polish 1 pound of gemstone in \(\frac{240}{1320}\) min ?????? We want to find the time it takes to polish a certain amount of gemstone not the other way round i.e. we are not interested in finding how many gemstones can be polished in a given time.
_________________
This is my response to the question and may be incorrect. Feel free to rectify any mistakes Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos



Director
Joined: 22 Jun 2019
Posts: 517
Followers: 4
Kudos [?]:
104
[1]
, given: 161

Re: Working together at their respective constant rates, robot A [#permalink]
13 Oct 2019, 01:22
1
This post received KUDOS
sandy wrote: Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is \(\frac{3}{5}\)that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?
(A) 15.75 (B) 18 (C) 18.75 (D) 27.5 (E) 30 Let, Efficiency of Robot B = 5e So, Efficiency of Robot A = 3e Combined efficiency of A and B is 8e = \(\frac{88}{6}\) pounds/min Or, e = \(\frac{11}{6}\) pounds/min So, Efficiency of A = \(\frac{33}{6}\) pound/min Thus, Time taken for robot A to polish 165 gemstones is \(\frac{165*6}{33}\) = 30 minutes, Answer must be (E)N:B: Collected From GMAT
_________________
New to the GRE, and GRE CLUB Forum? GRE: All About GRE  Search GRE Specific Questions  Download Vault Posting Rules: QUANTITATIVE  VERBAL
Questions' Banks and Collection: ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation.  ETS All Official Guides 3rd Party Resource's: All In One Resource's  All Quant Questions Collection  All Verbal Questions Collection  Manhattan 5lb All Questions Collection Books: All GRE Best Books Scores: Average GRE Score Required By Universities in the USA Tests: All Free & Paid Practice Tests  GRE Prep Club Tests Extra: Permutations, and Combination Vocab: GRE Vocabulary Facebook GRE Prep Group: Click here to join FB GRE Prep Group



Intern
Joined: 30 Apr 2020
Posts: 2
Followers: 0
Kudos [?]:
1
[1]
, given: 0

Re: Working together at their respective constant rates, robot A [#permalink]
30 Apr 2020, 04:14
1
This post received KUDOS
Can someone explain why the combined work formula doesn't work here? I understand your methodology, but keep getting 18 using that formula. Thanks!



GRE Instructor
Status: Entrepreneur  GMAT, GRE, CAT, SAT, ACT coach & mentor  Founder @CUBIX  Educonsulting  Content creator
Joined: 19 Jan 2020
Posts: 112
GMAT 1: 740 Q51 V39
GPA: 3.72
Followers: 5
Kudos [?]:
130
[2]
, given: 1

Re: Working together at their respective constant rates, robot A [#permalink]
30 Apr 2020, 05:33
2
This post received KUDOS
dsmaier wrote: Can someone explain why the combined work formula doesn't work here? I understand your methodology, but keep getting 18 using that formula. Thanks! Question: Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones? You wish to use combined work formula: Let us do it: Time taken by A and B to polish 88 pounds of gems = 6 minutes Let time by B to polish 88 pounds of gems = x min So time by A to polish 88 pounds of gems = 5x/3 min => time taken by A and B to polish 88 pounds of gems = (x)(5x/3)/(x + 5x/3) = 5x/8 minutes = 6 => x = 48/5 minutes => time by A to polish 88 pounds of gems = 5x/3 = 5/3 * 48/5 = 16 minutes => time by A to polish 1 pound of gems = 16/88 minutes => time by A to polish 165 pound of gems = 16/88 * 165 = 30 minutes Obviously, it doesn't make sense to do it like this, since it is lengthy So, let us improvise: Question: Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones? Rate of A = 3/5 of rate of B thus: If B polishes 5x gems per minute => A will polish 3x gems per minute => Together they polish 8x gems per minute thus, in 6 minutes they will polish 8x * 6 = 48x gems thus, this 48x is actually 88 thus: 88 gems is 48x => 165 gems is 48x/88 * 165 = 90x gems A was polishing 3x gems per minute So, time = 90x/3x = 30 minutes
_________________
Sujoy Kumar Datta  GMAT  Q51 & CAT (MBA @ IIM) 99.98 Overall with 99.99 QA IIT Kharagpur, TUD Germany LinkedIn: https://www.linkedin.com/in/sujoykumardatta/
Ping me for GRE & GMAT  Concepts & Strategy
Director  CUBIX (https://www.cubixprep.com)  OneClick (http://www.oneclickprep.com) Admissions Consulting: http://www.oneclickprep.com/admissionsconsulting/ _________ Email: sujoy.datta@gmail.com, Skype: sk_datta  Ask me anything about GRE



Intern
Joined: 30 Apr 2020
Posts: 2
Followers: 0
Kudos [?]:
1
[0], given: 0

Re: Working together at their respective constant rates, robot A [#permalink]
30 Apr 2020, 12:23
Thanks a ton  great seeing the comparison, much appreciated.



GRE Instructor
Joined: 10 Apr 2015
Posts: 3827
Followers: 148
Kudos [?]:
4472
[0], given: 69

Re: Working together at their respective constant rates, robot A [#permalink]
25 Aug 2020, 09:43
sandy wrote: Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is \(\frac{3}{5}\)that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?
(A) 15.75 (B) 18 (C) 18.75 (D) 27.5 (E) 30 Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes.rate = output/timeSo, if 88 pounds of gemstones are polished in 6 minutes, their combined RATE = 88/6 = 44/3 gemstones per minute Let A = robot A's RATE in gemstones per minute Let B = robot B's RATE in gemstones per minute We can now write: A + B = 44/3 gemstones per minute Robot A’s rate of polishing is 3/5 that of robot BSo, we can write: A = (3/5)B If we want to solve this equation for B, we can multiply both sides by 5/3 to get: (5/3)A = B Or we can express this as: B = 5A/3We can now take our original equation: A + B = 44/3And replace B with 5A/3 to get: A + 5A/3 = 44/3Let's eliminate the fractions by multiplying both sides of the equation by 3 to get: 3A + 5A = 44 Simplify: 8A = 44 Solve: A = 44/8 = 11/2In other words, robot A's RATE = 11/2 gemstones per minute How many minutes would it take robot A alone to polish 165 pounds of gemstones?time = output/rateSo, time = 165/( 11/2) = (165)(2/11) = 330/11 = 30 minutes Answer: E Cheers, Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course.
Sign up for GRE Question of the Day emails



Intern
Joined: 07 Jul 2020
Posts: 31
Followers: 0
Kudos [?]:
13
[0], given: 5

Re: Working together at their respective constant rates, robot A [#permalink]
25 Aug 2020, 10:26
Robot A and B can polish 88 pounds of gemstones in 6 minutes. So their combines rate is\(\frac{88}{6}\) We can write this as:
\(A+B = \frac{88}{6}\) where A and B are the rates of Robot A and Robot B respectively.
Now, we are told that obot A’s rate of polishing is \(\frac{3}{5}\) that of robot B. This can be written as:
\(B = \frac{5A}{3}\)
Substituting in our rate equation, we get: \(A+\frac{5A}{3}\) = \(\frac{88}{6}\)
Solving this, we get \(A = \frac{33}{6}\)
We know, \(Work = Rate * Time\) which implies \(Time = \frac{Work}{Rate}\)
plugging the values into this formula:
\(Time = \frac{165*6}{33}\) which is 30.
Therefore the answer is (E)



Intern
Joined: 08 Aug 2020
Posts: 43
Followers: 0
Kudos [?]:
30
[0], given: 4

Re: Working together at their respective constant rates, robot A [#permalink]
25 Aug 2020, 19:18
Since we were given that the rate of a is 3/5 of B This can be re written as ratio inform of A:B = 3:5 From the information above we can deduce that A polish 33 gems in 6mins while B Polish 55 gems Then we can say 33gems = 6mins Then 165gems = xmins Cross multiply this we have 165*6/33 Which equal to 30 Posted from my mobile device




Re: Working together at their respective constant rates, robot A
[#permalink]
25 Aug 2020, 19:18





