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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 ## Working alone, Manuel finishes cleaning tagged by: Brent@GMATPrepNow ##### This topic has 3 expert replies and 0 member replies ### Top Member ## Working alone, Manuel finishes cleaning Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together? A. 1.5 B. 2 C. 2.4 D. 3 E. 3.6 How many hours can Nick clean the house alone? I'm quite confused about it, can some experts explain? OA E ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply [quote="lheiannie07"]Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together? A. 1.5 B. 2 C. 2.4 D. 3 E. 3.6 How many hours can Nick clean the house alone? I'm quite confused about it, can some experts explain? OA E[/ quote] Hi lheiannie07, Let's take a look at your question. The question states that Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Let Nick take x hours to clean the entire house. -----(i) Manual finishes cleaning half the house in a third of the time Nick takes. So it will be (1/3)x to clean half the house. To clean the entire house the time would be double. Therefore, Manual will take (2/3)x to clean the entire house. ----(ii) The question states that Manuel alone cleans the entire house in 6 hours. But we know that Manual will take (2/3)x to clean the entire house from (ii), Hence, (2/3) x = 6 x = (6 x 3)/2 x = 18/2 x = 9 hours Where x actually represents the time Nick takes to clean the house. It means Nick takes 9 hours and Manual takes 6 hours to clean the entire house alone. Since rate and time is reciprocal of each other, therefore, we can now find the rate of cleaning the entire house of both Nick and Manual. Entire house cleaning rate of Nick = 1/9 Entire house cleaning rate of Nick = 1/6 Now we will find their combined rate if they work together. Combined cleaning rate of Noch and Manual if they work together = 1/9 + 1/6 = (2+3)/18 = 5/18 To find the total time Nick and Manual take to clean the entire house can be again calculated by finding the reciprocal of their combined rate. = 18/5 = 3.6 hours Hence, Option E is true. I am available if you'd like any followup. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply lheiannie07 wrote: Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together? A. 1.5 B. 2 C. 2.4 D. 3 E. 3.6 Another option for many work questions is to assign a nice value to the given job. Here, a nice value will be one that works well with the given numbers (6 hours, 1/2 the time, 1/3 of the time) So, have about 36. Let's say the entire job of cleaning the house consists of cleaning 36 rooms. Manuel alone cleans the ENTIRE house in 6 hours. So, Manuel can clean 36 rooms in 6 hours So, Manuel's RATE = 6 rooms per HOUR Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Half the house = 18 rooms Since Manuel's RATE is 6 rooms per hour, Manuel can clean 18 rooms in 3 hours We're told that this cleaning time is 1/3 of the time it takes Nick to clean the ENTIRE house alone So, it must take Nick 9 hours to clean the ENTIRE house alone The ENTIRE house consists of cleaning 36 rooms. Rate = output/time So, Nick's rate = 36/9 = 4 rooms per hour How many hours will it take Nick and Manuel to clean the entire house if they work TOGETHER? Manuel's RATE = 6 rooms per hour Nick's rate = 4 rooms per hour So, their COMBINED rate = 6 + 4 = 10 rooms per hour time = output/rate So, time = 36/10 = 3.6 hours Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these 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 Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 lheiannie07 wrote: Working alone, Manuel finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Manuel alone cleans the entire house in 6 hours. How many hours will it take Nick and Manuel to clean the entire house if they work together? A. 1.5 B. 2 C. 2.4 D. 3 E. 3.6 How many hours can Nick clean the house alone? I'm quite confused about it, can some experts explain? OA E Two important points to remember when solving work problems 1) rates are additive. If your rate is 'x' and my rate is 'y' our combined rate is x + y 2) rate and time have a reciprocal relationship. If you can do a job twice as fast as I can, you can do it in 1/2 the time. If Manuel can clean half the house in 1/3 of the time it takes Nick to clean the whole house, then Manuel can clean the whole house in 2/3 the time it takes Nick. If Manuel can do the house in 2/3 the time it takes Nick, then 6 = 2/3N, and Nick can clean the whole house in 9 hours To summarize - Manuel's rate = 1house/6 hour, or 1/6 Nick's rate = 1 house/9 hours, or 1/9 Their combined rate: 1/6 + 1/9 = 15/54 = 5/18; Their combined time is the reciprocal, or 18/5 = 3.6; The answer is E _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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