• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Running at their respective constant rates, machine X takes tagged by: Brent@GMATPrepNow ##### This topic has 4 expert replies and 0 member replies ## Running at their respective constant rates, machine X takes Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets. A. 4 B. 6 C. 8 D. 10 E. 12 OA is E Experts, may you help me here? I am confused. What formulas should I set here? ### GMAT/MBA Expert Senior | Next Rank: 100 Posts Joined 16 Dec 2014 Posted: 94 messages Followed by: 4 members Upvotes: 2 GMAT Score: 770 Top Reply Roland2rule wrote: Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets. A. 4 B. 6 C. 8 D. 10 E. 12 OA is E Experts, may you help me here? I am confused. What formulas should I set here? Work = Rate * Time Machine X: w = Rx * T Rx = w/T Machine Y: w = Ry * (T-2) Ry = w/(T-2) Situation from question: 5w/4 = (Rx + Ry)*3 5w/4 = [w/T + w/(T-2)]*3 --> we can divide through by W 5/4 = [1/T + 1/(T-2)]*3 5/12 = 1/T + 1/(T-2) 5(T)(T-2) = 12(T-2) + 12(T) 5T^2 - 10T = 24T - 24 5T^2 - 34T + 24 = 0 (T-6)(5T-4) = 0 T must be > 2 so the only solution is T = 6 Machine X can produce w widgets in T so it must be able to produce 2w widgets in 2T; given T= 6 then the answer is 2*6 = 12 Answer. E) 12 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12418 messages Followed by: 1244 members Upvotes: 5254 GMAT Score: 770 Roland2rule wrote: Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets. A. 4 B. 6 C. 8 D. 10 E. 12 Another approach is to assign a nice value to the job (w) Let's say that w = 12. GIVEN: Running at their respective constant rates, machine X takes 2 days longer to produce 12 widgets than machine Y Let t = time for machine Y to produce 12 widgets So, t+2 = time for machine X to produce 12 widgets RATE = output/time So, machine X's RATE = 12 widgets/(t + 2 days) = 12/(t+2) widgets per day And machine Y's RATE = 12 widgets/(t days) = 12/t widgets per day The two machines together produce 5w/4 widgets in 3 days In other words, The two machines together produce 5(12)/4 widgets in 3 days Or the two machines together produce 15 widgets in 3 days This means the COMBINED RATE = 5 widgets per day So, we can write: 12/(t+2) + 12/t = 5 Multiply both sides by (t+2)(t) to get: 12t + 12t + 24 = 5(t+2)(t) Simplify: 24t + 24 = 5tÂ˛ + 10t Rearrange: 5tÂ˛ - 14t - 24 = 0 Factor to get: (5t + 6)(t - 4) = 0 So, EITHER t = -6/5 OR t = 4 Since the time cannot be negative, it must be the case that t = 4 If t = 4, then it takes Machine Y 4 days to produce 12 widgets And it takes Machine X 6 days to produce 12 widgets How many days would it take machine X alone to produce 2w widgets? In other words, how many days would it take machine X alone to produce 24 widgets? (since w = 12) If it takes Machine X 6 days to produce 12 widgets, then it will take Machine X 12 days to produce 24 widgets Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 14925 messages Followed by: 1855 members Upvotes: 13060 GMAT Score: 790 Quote: Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y. At these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets? A) 4 B) 6 C) 8 D) 10 E) 12 Let w = 60 widgets, implying that (5/4)w = (5/4)(60) = 75 widgets. Since X and Y together can produce (5/4)w widgets in 3 days, the combined rate for X and Y = w/t = 75/3 = 25 widgets per day. We can PLUG IN THE ANSWERS, which represent X's time to produce 2w widgets. When the correct answer choice is plugged in, the combined rate for X and Y will be 25 widgets per day. D: 10 Here, X can produce 2w widgets in 10 days. Thus, the time for X to produce w widgets = 5 days. Since X takes 5 days to produce w=60 widgets, X's rate = w/t = 60/5 = 12 widgets per day. Since X takes 2 days longer than Y to produce w widgets, Y's time to produce w widgets = 3 days. Since Y takes 3 days to produce w=60 widgets, Y's rate = w/t = 60/3 = 20 widgets per day. Combined rate for X and Y = 12+20 = 32 widgets per day. Here, X and Y are working TOO FAST. Implication: X must take LONGER to produce 2w widgets, with the result that X and Y will work more SLOWLY. The correct answer is E. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1776 messages Followed by: 14 members Upvotes: 43 Roland2rule wrote: Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machines Y. AT these rates, if the two machines together produce 5w/4 widgets in 3 days, how many days would it take machine X alone to produce 2w widgets. A. 4 B. 6 C. 8 D. 10 E. 12 We can let x = the number of days it takes Machine X to produce w widgets and thus x - 2 = the number of days it takes Machine Y to produce w widgets. Furthermore, the rate of Machine X is w/x and the rate of Machine Y is w/(x - 2). We are given that they can produce 5w/4 widgets in 3 days. Thus, we have: 3(w/x) + 3[w/(x - 2)] = 5w/4 Dividing both sides by w, we have: 3/x + 3/(x - 2) = 5/4 Multiplying both sides by 4x(x - 2), we have: 12(x - 2) + 12x = 5x(x - 2) 12(x - 2) + 12x = 5x(x - 2) 12x - 24 + 12x = 5x^2 - 10x 5x^2 - 34x + 24 = 0 (5x - 4)(x - 6) = 0 x = 4/5 or x = 6 However, x canâ€™t be 4/5; if it were, y would be negative. Thus, x must be 6. Since it takes Machine X 6 days to produce w widgets, it will take 12 days to produce 2w widgets. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO • Award-winning private GMAT tutoring Register now and save up to$200

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• FREE GMAT Exam
Know how you'd score today for \$0

Available with Beat the GMAT members only code

### Top First Responders*

1 Brent@GMATPrepNow 68 first replies
2 fskilnik@GMATH 56 first replies
3 Jay@ManhattanReview 39 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 31 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik@GMATH

GMATH Teacher

130 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

101 posts
3 Max@Math Revolution

Math Revolution

84 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

79 posts
5 Jay@ManhattanReview

Manhattan Review

76 posts
See More Top Beat The GMAT Experts