GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Aug 2018, 18:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Francis can paint the house by himself in 6 hours, her brother Fred

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47983
Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

### Show Tags

21 Mar 2017, 05:35
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

72% (00:54) correct 28% (01:00) wrong based on 89 sessions

### HideShow timer Statistics

Francis can paint the house by himself in 6 hours, her brother Fred can paint the house in 4 hours, and her brother Frank can paint it in 9 hours. If they all worked together, what fraction of the house would be painted after one hour?

A. 1/36
B. 1/19
C. 1/2
D. 19/36
E. 36/19

_________________
CEO
Joined: 12 Sep 2015
Posts: 2706
Re: Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

### Show Tags

21 Mar 2017, 08:02
Top Contributor
Bunuel wrote:
Francis can paint the house by himself in 6 hours, her brother Fred can paint the house in 4 hours, and her brother Frank can paint it in 9 hours. If they all worked together, what fraction of the house would be painted after one hour?

A. 1/36
B. 1/19
C. 1/2
D. 19/36
E. 36/19

For work questions, there are two useful rules:

Rule #1: If a person can complete an entire job in k hours, then in one hour, the person can complete 1/k of the job
Example: If it takes Sue 5 hours to complete a job, then in one hour, she can complete 1/5 of the job. In other words, her work rate is 1/5 of the job per hour

Rule #2: If a person completes a/b of the job in one hour, then it will take b/a hours to complete the entire job
Example: If Sam can complete 1/8 of the job in one hour, then it will take him 8/1 hours to complete the job.
Likewise, if Joe can complete 2/3 of the job in one hour, then it will take him 3/2 hours to complete the job.

Let’s use these rules to solve the question. . . .

Francis can paint the house by himself in 6 hours
From Rule #1, we know that, in ONE HOUR, Francis can paint 1/6 of the house

Fred can paint the house in 4 hours
From Rule #1, we know that, in ONE HOUR, Fred can paint 1/4 of the house

Frank can paint the house in 9 hours
From Rule #1, we know that, in ONE HOUR, Frank can paint 1/9 of the house

If they all worked together, what fraction of the house would be painted after ONE HOUR?
Add each person's contribution for ONE HOUR:
1/6 + 1/4 + 1/9 = 6/36 + 9/36 + 4/36
= 19/36

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Founder of gmatprepnow.com

Intern
Joined: 12 Dec 2016
Posts: 10
Re: Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

### Show Tags

21 Mar 2017, 08:09
If we find the value that all 3 people mentioned do the job "together" in one hour, it actually is equal to the answer of the question;

hence : D
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3780
Location: India
GPA: 3.5
Re: Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

### Show Tags

21 Mar 2017, 08:37
Bunuel wrote:
Francis can paint the house by himself in 6 hours, her brother Fred can paint the house in 4 hours, and her brother Frank can paint it in 9 hours. If they all worked together, what fraction of the house would be painted after one hour?

A. 1/36
B. 1/19
C. 1/2
D. 19/36
E. 36/19

Let the total work be 36 units...

Efficiency of Francis is 6 units/hour
Efficiency of Fred is 9 units/hour
Efficiency of Frank is 4 units/hour

Combined efficiency of Francis , Fred and Frank is 19 units

So, part of house that would be painted after one hour is $$\frac{19}{36}$$

Thus, answer must be (D) $$\frac{19}{36}$$
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Non-Human User
Joined: 09 Sep 2013
Posts: 7761
Re: Francis can paint the house by himself in 6 hours, her brother Fred  [#permalink]

### Show Tags

27 Jul 2018, 09:48
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Francis can paint the house by himself in 6 hours, her brother Fred &nbs [#permalink] 27 Jul 2018, 09:48
Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.