Jun 29 07:00 AM PDT  09:00 AM PDT Learn reading strategies that can help even nonvoracious reader to master GMAT RC Jun 30 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Jul 01 08:00 AM PDT  09:00 AM PDT Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Jul 01 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 07 Apr 2014
Posts: 104

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
11 Sep 2014, 06:18
Walkabout wrote: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y) (B) y/(x+y) (C) xy/(x+y) (D) xy/(xy) (E) xy/(yx) 1/a  rate of machine A for an hour 1/brate of machine B for an hour 1/x = 1/a +1/b for an hour if working alone A 's rate is 1/a = 1/y for an hour 1/y+1/b = 1/x b = xy/yx



Board of Directors
Joined: 17 Jul 2014
Posts: 2540
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
13 Oct 2014, 10:31
I did not do the long way or the bunuel's method I knew that machine B must be the difference between y and x the only solution that has yx is E therefore I picked E without even solving anything. is this method ok to use? :D



Intern
Joined: 21 Apr 2014
Posts: 39

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
13 Oct 2014, 13:57
What we are really looking for is what number multiplied by B(rate) equals 800. In short, Brate*t=800, because rate multiplied by time equals work we need to find t in terms of x and y and we are given 2 clues. 1) "Machines A and B produce 800 nails in x hours" in mathematical notation: (Arate+Brate)*x=800 nails 2) "Machine A produces 800 nails in y hours" i.e. Arate*y=800 nails We can substitute 2 into 1 by dividing both sides of 1 by x giving us: (Arate+Brate)=800/x Then dividing both sides of 2 by y and isolating Arate, giving us Arate=800/y putting 2 into 1, we get 800/y+Brate=800/x lets put the 800s together by subtracting 800/y from both sides and getting Brate =(800/x)(800/y) we can simplify the right side of the equation and get (800y800x)/xy multiply both sides of the equation by xy and you get Brate*xy=800(yx) then divide both sides by yx and you get Brate*xy/(yx)=800 This means that t= xy/(yx) (E), because Brate*t=800
_________________



Intern
Joined: 23 Sep 2014
Posts: 13

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
14 Oct 2014, 05:34
These are the type of questions that make me feel like i wont be able to get a good score on the GMAT. I couldnt solve this at all, let alone solve it in 2 minutes. Still quite confused about the smart numbers in this case.



Senior Manager
Joined: 10 Mar 2013
Posts: 488
Location: Germany
Concentration: Finance, Entrepreneurship
GPA: 3.88
WE: Information Technology (Consulting)

Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
17 Aug 2015, 04:44
Hi, here is one more approach with smart numbers Rate A=100 >Ty=800/100=8 Rate B=100 >Tb=800/100=8 Rate A+B=200 >Tx=800/200=4 Plug in this numbers in the answer choices and you'll see that only answer (E) is the correct answer >XY/(YX)=(8*4)/(84)=8
_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.
Share some Kudos, if my posts help you. Thank you !
800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50 GMAT PREP 670 MGMAT CAT 630 KAPLAN CAT 660



Intern
Joined: 02 Jun 2015
Posts: 20
Location: United States

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
13 May 2016, 10:56
W= AxB/A+B 3x6/3+6 = 18/9 = 2 (together A and B produce 800 nails in 2 hours, x=2) (A produce 800 nails in 3 hours, y=3) (B produce 800 nails in 6 hours, find a match in the answer choice=6) A) 2/5 not a match B) 3/5 not a match C) 6/5 not a match D) 6/1=6 not a match E) 6/1 = 6 correct answer HINT: When it comes to work formula and you're dealing with variables, the perfect numbers to plug in this formula are 3 and 6. Hope it helps



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6681
Location: United States (CA)

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
01 Jun 2016, 07:41
This problem is what we call a combined worker problem, where Work (of machine 1) + Work (of machine 2) = Total Work Completed In this case, Work (of Machine A) + Work (of Machine B) = 800 We know that Machines A and B produce 800 nails in x hours. Thus, the TIME that Machine A and B work together is x hours. We are also given that Machine A produces 800 nails in y hours. Thus, the rate for Machine A is 800/y. Since we do not know the rate for Machine B, we can label its rate as 800/B, where B is the number of hours it takes Machine B to produce 800 nails. To better organize our information we can set up a rate x time = work matrix: We now can say: Work (of Machine A) + Work (of Machine B) = 800 800x/y + 800x/B = 800 To cancel out the denominators, we can multiply the entire equation by yB. This gives us: 800xB + 800xy= 800yB xB + xy = yB xy = yB – xB xy = B(y – x) xy /(y – x) = B Answer: E
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Current Student
Joined: 20 Jan 2017
Posts: 57
Location: United States (NY)
GMAT 1: 750 Q48 V44 GMAT 2: 610 Q34 V41
GPA: 3.92

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
31 Jan 2017, 04:49
1) \((A+B)*x=800; A+B=\frac{800}{x}\) 2) \(A*y=800; A=\frac{800}{y}\) 3) \(B=(A+B)A=\frac{800}{x}\frac{800}{y}=\frac{800}{(800y800x)/xy}=\frac{800xy}{800(yx)}=\frac{xy}{(yx)}\)
The correct answer is E



Manager
Joined: 27 Dec 2016
Posts: 232
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
22 Apr 2017, 16:33
Walkabout wrote: Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
(A) x/(x+y) (B) y/(x+y) (C) xy/(x+y) (D) xy/(xy) (E) xy/(yx) Solved in under 2 minutes. First,
We should know what is the question? Asking B time. Second,
Since Time = \(\frac{Work}{Rate}\) and we already know that work = 800, so we must calculate Rate. Third,Rate B = Rate combined  Rate A = [\(\frac{800}{x}\)]  [\(\frac{800}{y}\)] = \(\frac{800 (yx)}{(xy)}\) Hence, we can calculate Time = 800 * \(\frac{(xy)}{800 (yx)}\). We can eliminate 800 so answer is = \(\frac{xy}{(yx)}\), E.
_________________
There's an app for that  Steve Jobs.



Intern
Joined: 19 Mar 2015
Posts: 15
Location: India

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
03 Jun 2017, 06:44
Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in y hours. In terms of x and y, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails?
Sollution : (A+B)*X=A*Y B= (YX)/X (1) B*Z=A*Y B = (A*Y)/Z (2)
From (1) & (2) (A*Y)/Z = (YX)/X Z = (Y*X)/(YX)



Manager
Joined: 07 Jun 2017
Posts: 166
Location: India
Concentration: Technology, General Management
GPA: 3.6
WE: Information Technology (Computer Software)

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
19 Sep 2017, 22:07
here 800 nails can be taken as "one" work. then together they are taking x hours A alone taking Y hours then B alone can be obtained by 1/B = 1/X1/Y 1/B = YX/XY b= XY/YX
_________________
Regards, Naveen email: nkmungila@gmail.com Please press kudos if you like this post



VP
Joined: 09 Mar 2016
Posts: 1274

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
21 Nov 2017, 07:05
Bunuel wrote: gciftci wrote: Q: I get the algebra but I got confused with this question because I thaught adding and deviding rates was a NoNo? Why is it diffrent in this case? No, we CAN easily sum the rates. For example: If we are told that A can complete a job in 2 hours and B can complete the same job in 3 hours, then A's rate is 1/2 job/hour and B's rate is 1/3 job/hour. The combined rate of A and B working simultaneously would be 1/2+1/3=5/6 job/hours, which means that the will complete 5/6 job in hour working together. THEORYThere are several important things you should know to solve work problems: 1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.\(time*speed=distance\) <> \(time*rate=job \ done\). For example when we are told that a man can do a certain job in 3 hours we can write: \(3*rate=1\) > \(rate=\frac{1}{3}\) job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then \(5*(2*rate)=1\) > so rate of 1 printer is \(rate=\frac{1}{10}\) job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then \(3*(2*rate)=12\) > so rate of 1 printer is \(rate=2\) pages per hour; So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job > 1/6 of the job will be done in 1 hour (rate). 2. We can sum the rates.If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is \(rate_a=\frac{job}{time}=\frac{1}{2}\) job/hour and B's rate is \(rate_b=\frac{job}{time}=\frac{1}{3}\) job/hour. Combined rate of A and B working simultaneously would be \(rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\) job/hour, which means that they will complete \(\frac{5}{6}\) job in one hour working together. 3. For multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.For example if: Time needed for A to complete the job is A hours; Time needed for B to complete the job is B hours; Time needed for C to complete the job is C hours; ... Time needed for N to complete the job is N hours; Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously. For two and three entities (workers, pumps, ...): General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)). General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:\(T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3}\) hours. Some work problems with solutions: http://gmatclub.com/forum/timenworkp ... cal%20ratehttp://gmatclub.com/forum/facingproble ... reciprocalhttp://gmatclub.com/forum/whatamidoi ... reciprocalhttp://gmatclub.com/forum/gmatprepps ... cal%20ratehttp://gmatclub.com/forum/questionsfro ... cal%20ratehttp://gmatclub.com/forum/agoodone98 ... hilit=ratehttp://gmatclub.com/forum/solutionrequ ... ate%20donehttp://gmatclub.com/forum/workproblem ... ate%20donehttp://gmatclub.com/forum/hourstotype ... ation.%20RHope this helps Bunuel hello, great explantation. Just trying to understand when you multiply 3 * rate =1 how do go get 1 ? also when you multiply 3 (2*rate) =12 how did you get 12 ? and what number is implied by RATE ? Big thanks for brilliant explanation in advance and have great day!



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
21 Nov 2017, 07:27
dave13 wrote: Bunuel wrote: gciftci wrote: Q: I get the algebra but I got confused with this question because I thaught adding and deviding rates was a NoNo? Why is it diffrent in this case? No, we CAN easily sum the rates. For example: If we are told that A can complete a job in 2 hours and B can complete the same job in 3 hours, then A's rate is 1/2 job/hour and B's rate is 1/3 job/hour. The combined rate of A and B working simultaneously would be 1/2+1/3=5/6 job/hours, which means that the will complete 5/6 job in hour working together. THEORYThere are several important things you should know to solve work problems: 1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.\(time*speed=distance\) <> \(time*rate=job \ done\). For example when we are told that a man can do a certain job in 3 hours we can write: \(3*rate=1\) > \(rate=\frac{1}{3}\) job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then \(5*(2*rate)=1\) > so rate of 1 printer is \(rate=\frac{1}{10}\) job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then \(3*(2*rate)=12\) > so rate of 1 printer is \(rate=2\) pages per hour; So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job > 1/6 of the job will be done in 1 hour (rate). 2. We can sum the rates.If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is \(rate_a=\frac{job}{time}=\frac{1}{2}\) job/hour and B's rate is \(rate_b=\frac{job}{time}=\frac{1}{3}\) job/hour. Combined rate of A and B working simultaneously would be \(rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\) job/hour, which means that they will complete \(\frac{5}{6}\) job in one hour working together. 3. For multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.For example if: Time needed for A to complete the job is A hours; Time needed for B to complete the job is B hours; Time needed for C to complete the job is C hours; ... Time needed for N to complete the job is N hours; Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously. For two and three entities (workers, pumps, ...): General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)). General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:\(T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3}\) hours. Some work problems with solutions: http://gmatclub.com/forum/timenworkp ... cal%20ratehttp://gmatclub.com/forum/facingproble ... reciprocalhttp://gmatclub.com/forum/whatamidoi ... reciprocalhttp://gmatclub.com/forum/gmatprepps ... cal%20ratehttp://gmatclub.com/forum/questionsfro ... cal%20ratehttp://gmatclub.com/forum/agoodone98 ... hilit=ratehttp://gmatclub.com/forum/solutionrequ ... ate%20donehttp://gmatclub.com/forum/workproblem ... ate%20donehttp://gmatclub.com/forum/hourstotype ... ation.%20RHope this helps Bunuel hello, great explantation. Just trying to understand when you multiply 3 * rate =1 how do go get 1 ? also when you multiply 3 (2*rate) =12 how did you get 12 ? and what number is implied by RATE ? Big thanks for brilliant explanation in advance and have great day! We are equating to the amount of job: 1 job, 12 pages, etc. For more check: 17. Work/Rate Problems On other subjects: ALL YOU NEED FOR QUANT ! ! !Ultimate GMAT Quantitative MegathreadHope it helps.
_________________



VP
Joined: 09 Mar 2016
Posts: 1274

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
23 Nov 2017, 09:36
khairilthegreat wrote: RateA + RateB = 800/x
RateA = 800/y RateB = 800/z
So > 800/y + 800/z = 800/x
1/y + 1/z = 1/x > 1/z = 1/x  1/y z = xy/(yx) how did you get from 1/z = 1/x  1/y this one z = xy/(yx) ? can you please explain step by step ?



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
23 Nov 2017, 09:40
dave13 wrote: khairilthegreat wrote: RateA + RateB = 800/x
RateA = 800/y RateB = 800/z
So > 800/y + 800/z = 800/x
1/y + 1/z = 1/x > 1/z = 1/x  1/y z = xy/(yx) how did you get from 1/z = 1/x  1/y this one z = xy/(yx) ? can you please explain step by step ? Basic algebraic manipulations: \(\frac{1}{z} = \frac{1}{x}  \frac{1}{y}\) \(\frac{1}{z} = \frac{yx}{xy}\) \(z=\frac{xy}{yx}\)
_________________



VP
Joined: 09 Mar 2016
Posts: 1274

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
23 Nov 2017, 09:52
Bunuel wrote: gciftci wrote: Q: I get the algebra but I got confused with this question because I thaught adding and deviding rates was a NoNo? Why is it diffrent in this case? No, we CAN easily sum the rates. For example: If we are told that A can complete a job in 2 hours and B can complete the same job in 3 hours, then A's rate is 1/2 job/hour and B's rate is 1/3 job/hour. The combined rate of A and B working simultaneously would be 1/2+1/3=5/6 job/hours, which means that the will complete 5/6 job in hour working together. THEORYThere are several important things you should know to solve work problems: 1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.\(time*speed=distance\) <> \(time*rate=job \ done\). For example when we are told that a man can do a certain job in 3 hours we can write: \(3*rate=1\) > \(rate=\frac{1}{3}\) job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then \(5*(2*rate)=1\) > so rate of 1 printer is \(rate=\frac{1}{10}\) job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then \(3*(2*rate)=12\) > so rate of 1 printer is \(rate=2\) pages per hour; So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job > 1/6 of the job will be done in 1 hour (rate). 2. We can sum the rates.If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is \(rate_a=\frac{job}{time}=\frac{1}{2}\) job/hour and B's rate is \(rate_b=\frac{job}{time}=\frac{1}{3}\) job/hour. Combined rate of A and B working simultaneously would be \(rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}\) job/hour, which means that they will complete \(\frac{5}{6}\) job in one hour working together. 3. For multiple entities: \(\frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}\), where \(T\) is time needed for these entities to complete a given job working simultaneously.For example if: Time needed for A to complete the job is A hours; Time needed for B to complete the job is B hours; Time needed for C to complete the job is C hours; ... Time needed for N to complete the job is N hours; Then: \(\frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}\), where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously. For two and three entities (workers, pumps, ...): General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:Given that \(t_1\) and \(t_2\) are the respective individual times needed for \(A\) and \(B\) workers (pumps, ...) to complete the job, then time needed for \(A\) and \(B\) working simultaneously to complete the job equals to \(T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2}\) hours, which is reciprocal of the sum of their respective rates (\(\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}\)). General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:\(T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3}\) hours. Some work problems with solutions: http://gmatclub.com/forum/timenworkp ... cal%20ratehttp://gmatclub.com/forum/facingproble ... reciprocalhttp://gmatclub.com/forum/whatamidoi ... reciprocalhttp://gmatclub.com/forum/gmatprepps ... cal%20ratehttp://gmatclub.com/forum/questionsfro ... cal%20ratehttp://gmatclub.com/forum/agoodone98 ... hilit=ratehttp://gmatclub.com/forum/solutionrequ ... ate%20donehttp://gmatclub.com/forum/workproblem ... ate%20donehttp://gmatclub.com/forum/hourstotype ... ation.%20RHope this helps it helps thanks! one of the links to similar topic you shared is locked, so I could not post a question there: here it is https://gmatclub.com/forum/ittakes6d ... cal%20rate (I couldn't understand how m/3+5=w/9 to solve for M and W in your solution, Also I couldn't understand why in the second equation you wrote  M/3 and not 3/m  As per formula Time = JOB / RATE and Rate = Job / time so in both cases in the numerator is JOB and not TIME  I wanted to ask a question but couldn't since the topic is locked )



VP
Joined: 09 Mar 2016
Posts: 1274

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
23 Nov 2017, 10:14
Bunuel wrote: dave13 wrote: khairilthegreat wrote: RateA + RateB = 800/x
RateA = 800/y RateB = 800/z
So > 800/y + 800/z = 800/x
1/y + 1/z = 1/x > 1/z = 1/x  1/y z = xy/(yx) how did you get from 1/z = 1/x  1/y this one z = xy/(yx) ? can you please explain step by step ? Basic algebraic manipulations: \(\frac{1}{z} = \frac{1}{x}  \frac{1}{y}\) \(\frac{1}{z} = \frac{yx}{xy}\) \(z=\frac{xy}{yx}\) Bunuel thanks! one question how after this \(\frac{1}{z} = \frac{yx}{xy}\) you got this \(z=\frac{xy}{yx}\)[/quote] ? please say in words what you did



Math Expert
Joined: 02 Sep 2009
Posts: 55804

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
23 Nov 2017, 10:23
dave13 wrote: Bunuel thanks! one question how after this \(\frac{1}{z} = \frac{yx}{xy}\) you got this \(z=\frac{xy}{yx}\)? please say in words what you did You really should brushup fundamentals before attempting questions. \(z=\frac{xy}{yx}\) Crossmultiple: \(z(yx)=xy\) Divide by yx: \(z=\frac{xy}{yx}\)
_________________



Intern
Joined: 30 May 2017
Posts: 11
Location: India
Concentration: Finance, Strategy
GPA: 4
WE: Engineering (Venture Capital)

Re: Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
01 Sep 2018, 22:58
Why to make answer complicated when the logic is simple ! X hours for both A and B to produce 800 nails So time = x hours Work = 800 We know rate = work/ time So rate of A+B = 800/x Now time for A = y hours and work = 800 So rate of A= 800/y We know rates can be added or subtracted for the same amount of work Hence rate of (A+B) = Rate of A + Rate of B So Rate of B = Rate of (A+B)  Rate of A which is equal to (800/x)  800/y which leads to 800(yx)/xy So rate of B = Work of B/ Time for B So time = Work/ Rate which is equal to 800/[800(yx)/xy] Simplifying will give xy/(yx) Cheers for the Kudos !
_________________
You say this is a problem , I say this must be an opportunity



Intern
Joined: 28 Apr 2016
Posts: 42
Location: United States
GPA: 3.9

Working simultaneously at their respective constant rates, M
[#permalink]
Show Tags
Updated on: 20 Oct 2018, 06:22
The solutions in this thread show that there are multiple ways to answer this question. Below are tips that you can use for a couple of different approaches (the links go to pages with lists of questions that you can use to practice each tip): Rate problems: Use D = R x T and W = R x T: In this question, it's probably most useful to use the variations R = W/T and T = W/R, because you are given 2 rates (A + B = 800/x and A = 800/y), and you really need to solve for B, because the question asks you for the time taken by Machine B, which is 800/B. You can subtract the second rate equation from the first rate equation to solve for B, then simplify this and plug it into 800/B to get the answer. Set the amount of work equal to 1 for a single job: As pointed out by others on this thread, because the amount of work done (800 nails) is always the same, we can simplify our calculations even more by just calling this a single job and setting the amount of work equal to 1, instead of 800. Add rates when they are simultaneous: When we are talking about two simultaneous rates, such as Machines A and B working together, it's important to realize that we can add the rates to get their combined rate. This is what allows us to say that the combined rate is A+B, if the rates for each machine are A and B. Pick smart numbers to plug into variables in answer choices: When you see that the answer choices contain variables, an alternative approach is to choose smart numbers to plug in for each variable. You also need to know what value you need to get after you plug in the numbers, so that you can eliminate any answer choices that don't give you that value. One really easy scenario to use is one where each machine produces 400 nails per hour (this is equivalent to what Bunuel used in his smart numbers solution), in which case x = 1 and y = 2, and the final value needs to be 2 hours. When you plug x = 1 and y = 2 into the answer choices, E is the only one that gives an value of 2 hours, so that is the correct answer. Note that, if more than one answer choice gave you the correct value, you would need to choose another set of numbers and plug them into the remaining answer choices. Please let me know if you have any questions, or if you want me to post a video solution!
_________________
Online GMAT tutor with a 780 GMAT score. Harvard graduate. Please read and share my free GMAT Timing Strategy Guide!
Originally posted by JeffYin on 13 Oct 2018, 12:47.
Last edited by JeffYin on 20 Oct 2018, 06:22, edited 1 time in total.




Working simultaneously at their respective constant rates, M
[#permalink]
13 Oct 2018, 12:47



Go to page
Previous
1 2 3
Next
[ 42 posts ]



