• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 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 Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

Working alone, Manuel finishes cleaning

This topic has 3 expert replies and 0 member replies

Working alone, Manuel finishes cleaning

Post
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

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Top Reply
Post
[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.

  • +1 Upvote Post
  • Quote
  • Flag
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

Top Reply
Post
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 – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’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
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh

Top First Responders*

1 Ian Stewart 53 first replies
2 Brent@GMATPrepNow 36 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 25 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

90 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

76 posts
4 image description Ian Stewart

GMATiX Teacher

62 posts
5 image description GMATGuruNY

The Princeton Review Teacher

44 posts
See More Top Beat The GMAT Experts