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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 ## If 6 workers can build 4 cars in 2 days, then how many days ##### This topic has 5 expert replies and 0 member replies ## If 6 workers can build 4 cars in 2 days, then how many days If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars? (A) 5/3 (B) 9/4 (C) 8/3 (D) 11/4 (E) 10/3 I'm confused how to set up the formulas here. Can any experts help? ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi ardz24, We're told that 6 workers can build 4 cars in 2 days. We're asked for the number of days needed for 8 workers to build 6 cars. In these types of 'Work' questions, it helps to think in terms of the TOTAL work needed to complete a task. Here, we have 6 workers who EACH work for 2 days. That would be... (6 workers)(2 days of work each) = 12 worker-days of effort needed to build 4 cars. In other words... (12 worker-days)/(4 cars) = 3 worker-days per car Thus, 1 worker could build a car in 3 days 2 workers could build a car in 1.5 days 3 workers could build a car in 1 day Etc. We're asked for the number of days it would take 8 workers to build 6 cars. The 6 cars would require.... (6 cars)(3 worker-days each) = 18 worker-days of effort With 8 workers, the work required by EACH would be.... (18 worker-days of effort)/(8 workers) = 18/8 = 9/4 total days Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert Legendary Member Joined 20 Jul 2017 Posted: 503 messages Followed by: 11 members Upvotes: 86 GMAT Score: 770 Top Reply To use the rate formula, we can go through a process like this: We know that our rate formula is 1/A + 1/B = 1/A and B, where A is the amount of time worker A takes to finish a job alone, B is the amount of time worker B takes to finish a job alone, and A and B is the amount of time workers A and B take to finish a job together. We can use this formula for as many workers as we want. Here, we have six workers, so we use the equation 1/A + 1/B + 1/C + 1/D + 1/E + 1/F = 1/A, B, C, D, E, and F. We know that the six workers build 4 cars in 2 days. This also means that they build 1 car in 1/2 days. So we'll fill in 1/2 for A, B, C, D, E, and F: 1/A + 1/B + 1/C + 1/D + 1/E + 1/F = 1/(1/2) We assume that all individual workers work at the same pace, so we'll call the number of days it takes for a single worker to build 1 car x: 1/x + 1/x + 1/x + 1/x + 1/x + 1/x = 2 6/x = 2 Now we solve for x: x = 2 So we know it takes a single worker 3 days to build 1 car. Let's set up an equation for how long it would take 8 workers to build one car: 8(1/3) = 1/A, B, C, D, E, F, G, and H Now we solve for the number of days is would take 8 workers to build one car: 8/3 = 1/A, B, C, D, E, F, G, and H 1/A, B, C, D, E, F, G, and H = 3/8 So it would take 8 workers 3/8 of a day to build 1 car. To find the number of days it would take to build 6 cars, we multiply by 6: 3/8 * 6 = 18/8 = 9/4 So it would take 8 workers 9/4 days to build 6 cars. We can also go through this logically by understanding that time will be proportional to number of cars and inversely proportional to number of workers: 6 workers 4 cars = 2 days 1 worker 4 cars = 2 * 6 = 12 days 1 worker 1 car = 12 / 4 = 3 days 1 worker 6 cars = 3 * 6 = 18 days 8 workers 6 cars = 18 / 8 = 9/4 days _________________ Erika John - Content Manager/Lead Instructor https://gmat.prepscholar.com/gmat/s/ Get tutoring from me or another PrepScholar GMAT expert: https://gmat.prepscholar.com/gmat/s/tutoring/ Learn about our exclusive savings for BTG members (up to 25% off) and our 5 day free trial Check out our PrepScholar GMAT YouTube channel, and read our expert guides on the PrepScholar GMAT blog ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15353 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 ardz24 wrote: If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars? (A) 5/3 (B) 9/4 (C) 8/3 (D) 11/4 (E) 10/3 We can use the following equation: (workers * days)/output = (workers * days)/output. Since 6 workers take 2 days to produce 4 cars, and we must calculate the number of days for 8 workers to produce 6 cars, we get: (6*2)/4 = (8x)/6 3 = 4x/3 9 = 4x 9/4 = x. The correct answer is B. _________________ 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 Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 ardz24 wrote: If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars? (A) 5/3 (B) 9/4 (C) 8/3 (D) 11/4 (E) 10/3 I'm confused how to set up the formulas here. Can any experts help? Another way to think about it: First, if 6 workers can do 4 cars in 2 days (or 2 cars in 1 day), we know they can do 6 cars in 3 days. Next, know that Time and # of workers will have a reciprocal relationship. If we have twice as many workers, it will take 1/2 the time, etc. So if we have 8/6 as many workers, it will take them 6/8 the time. If 6 workers could do 6 cars in 3 days, then 8 workers will do 6 cars in 6/8 the time, or (6/8) * 3 days = 9/4 days. The answer is B _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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BTGmoderatorAT wrote:
If 6 workers can build 4 cars in 2 days, then how many days would it take 8 workers to build 6 cars?

(A) 5/3
(B) 9/4
(C) 8/3
(D) 11/4
(E) 10/3
We know the rate of 6 workers is 4/2 = 2 cars/day. We can create a proportion to determine the rate of the 8 workers.

6/2 = 8/x

3 = 8/x

3x = 8

x = 8/3

Thus, it will take 8 workers 6/(8/3)= 18/8 = 9/4 days to build 6 cars.

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Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com

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