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Re: Working simultaneously at their respective constant rates, M
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11 Sep 2014, 05:18
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



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Re: Working simultaneously at their respective constant rates, M
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13 Oct 2014, 09:31
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



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Re: Working simultaneously at their respective constant rates, M
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13 Oct 2014, 12:57
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
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Re: Working simultaneously at their respective constant rates, M
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14 Oct 2014, 04:34
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.



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Working simultaneously at their respective constant rates, M
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17 Aug 2015, 03:44
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
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Re: Working simultaneously at their respective constant rates, M
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13 May 2016, 09:56
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



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Re: Working simultaneously at their respective constant rates, M
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01 Jun 2016, 06:41
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
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Re: Working simultaneously at their respective constant rates, M
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31 Jan 2017, 03:49
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



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Re: Working simultaneously at their respective constant rates, M
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22 Apr 2017, 15:33
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.
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Re: Working simultaneously at their respective constant rates, M
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03 Jun 2017, 05:44
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)



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Re: Working simultaneously at their respective constant rates, M
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19 Sep 2017, 21:07
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
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Re: Working simultaneously at their respective constant rates, M
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21 Nov 2017, 06:05
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!



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Re: Working simultaneously at their respective constant rates, M
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21 Nov 2017, 06:27
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.
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Re: Working simultaneously at their respective constant rates, M
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23 Nov 2017, 08:36
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 ?



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Re: Working simultaneously at their respective constant rates, M
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Re: Working simultaneously at their respective constant rates, M
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23 Nov 2017, 08:52
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 )



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Re: Working simultaneously at their respective constant rates, M
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23 Nov 2017, 09:14
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



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Re: Working simultaneously at their respective constant rates, M
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Re: Working simultaneously at their respective constant rates, M
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01 Sep 2018, 21:58
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 !
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Working simultaneously at their respective constant rates, M
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Updated on: 20 Oct 2018, 05:22
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!
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Originally posted by JeffYin on 13 Oct 2018, 11:47.
Last edited by JeffYin on 20 Oct 2018, 05:22, edited 1 time in total.




Working simultaneously at their respective constant rates, M &nbs
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13 Oct 2018, 11:47



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