GMAT Changed on April 16th - Read about the latest changes here

It is currently 23 Apr 2018, 04:45

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

New homeowners Jo and Colin are painting their basement. Working alone

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44628
New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

Show Tags

New post 08 Aug 2017, 01:12
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

69% (01:39) correct 31% (01:58) wrong based on 128 sessions

HideShow timer Statistics

New homeowners Jo and Colin are painting their basement. Working alone, Jo could paint the entire basement in seven hours; working alone, Colin could paint it in six. They work together at their separate and constant rates for two hours; then Colin goes to work at his office while Jo continues to paint. How long in hours and minutes will it take for the basement to be completely painted?

A. 3:00
B. 3:30
C. 4:00
D. 4:18
E. 4:40
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Director
Director
User avatar
P
Joined: 18 Aug 2016
Posts: 631
GMAT ToolKit User Premium Member Reviews Badge
Re: New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

Show Tags

New post 08 Aug 2017, 01:23
1
This post received
KUDOS
Bunuel wrote:
New homeowners Jo and Colin are painting their basement. Working alone, Jo could paint the entire basement in seven hours; working alone, Colin could paint it in six. They work together at their separate and constant rates for two hours; then Colin goes to work at his office while Jo continues to paint. How long in hours and minutes will it take for the basement to be completely painted?

A. 3:00
B. 3:30
C. 4:00
D. 4:18
E. 4:40


Let the work be 42 units
Jo does 6 units/hour
Colin does 7 units/hour
In 2 hours together they finish 26 units (12+14)
Leftover is 16 units of work which Jo has to finish
Jo will finish it in 2 hrs 40 minutes
Total time for basement to be completely finished is 2 hrs+2hrs 40 mins = 4 hrs 40 mins
E
_________________

We must try to achieve the best within us


Thanks
Luckisnoexcuse

1 KUDOS received
SC Moderator
avatar
D
Joined: 22 May 2016
Posts: 1551
Premium Member CAT Tests
New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

Show Tags

New post 08 Aug 2017, 05:24
1
This post received
KUDOS
Bunuel wrote:
New homeowners Jo and Colin are painting their basement. Working alone, Jo could paint the entire basement in seven hours; working alone, Colin could paint it in six. They work together at their separate and constant rates for two hours; then Colin goes to work at his office while Jo continues to paint. How long in hours and minutes will it take for the basement to be completely painted?

A. 3:00
B. 3:30
C. 4:00
D. 4:18
E. 4:40

1) First segment of work: together

Jo's rate = 6 (or \(\frac{1}{6}\), see end of post) and Colin's rate = 7 (or \(\frac{1}{7}\))

Combined rate**: \(\frac{(a+b)}{ab}\) = \(\frac{(6+7)}{(6*7)}\) =\(\frac{13}{42}\)

Two hours together, \(rt=W\):

\(\frac{13}{42}\) * 2 = \(\frac{26}{42}\) or \(\frac{13}{21}\) of work is finished.

Work remaining: \(\frac{8}{21}\)

2) Second segment of work, Jo alone. \(\frac{W}{r} = t\) for Jo to finish

(8/21)/(1/7) = \(\frac{8}{21}\)*\(\frac{7}{1}\) = \(\frac{8}{3}\) hrs. Jo alone = 2\(\frac{2}{3}\) hrs

3) Total time: 2 + 2\(\frac{2}{3}\) = 4\(\frac{2}{3}\) hrs is 4 hrs 40 minutes, or 4:40

Answer E

** The formula is ubiquitous here. I haven't seen it explained often, but I am not adept at the search function. Just in case, the formula comes from adding rates:\(\frac{1}{6}\) +\(\frac{1}{7}\) = \(\frac{13}{42}\) (add 6 and 7 for numerator, multiply 6 and 7 for denominator).
_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

Expert Post
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2447
Location: United States (CA)
Re: New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

Show Tags

New post 10 Aug 2017, 10:47
Bunuel wrote:
New homeowners Jo and Colin are painting their basement. Working alone, Jo could paint the entire basement in seven hours; working alone, Colin could paint it in six. They work together at their separate and constant rates for two hours; then Colin goes to work at his office while Jo continues to paint. How long in hours and minutes will it take for the basement to be completely painted?

A. 3:00
B. 3:30
C. 4:00
D. 4:18
E. 4:40


We are given that Jo’s rate = 1/7 and Colin’s rate = 1/6.

Since they both work together for 2 hours and Jo finishes the job, if we let x = the extra time Jo works, we know that Colin worked for 2 hours and Jo worked for (2 + x) hours. We can create the following equation to determine x:

(1/6)(2) + (1/7)(2 + x) = 1

2/6 + (2+x)/7 = 1

Multiplying by 42, we have:

14 + 6(2 + x) = 42

14 + 12 + 6x = 42

6x = 16

x = 16/6 = 2 ⅔

So, it takes 2 + ⅔ = 4⅔ hours or 4 hours and 40 minutes to complete the entire job.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

1 KUDOS received
Intern
Intern
avatar
B
Joined: 20 Jun 2016
Posts: 45
Re: New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

Show Tags

New post 14 Aug 2017, 00:15
1
This post received
KUDOS
1
This post was
BOOKMARKED
Joe takes 7 hours to complete the work.
Colin takes 6 hours to complete the work.

Let us take the LCM of the two= 42 units.

Joe does 6 units of work per hour.
Colin does 7 units of work per hour.

Together they do 13 hours of work per hour.
Therefore in 2 hours they do= 26 units of work.

Remaining units of work needs to be finished by Joe after Colin leaves.

Therefore work remaining= 16 units.
Number of units of work done by Joe per hour= 6 units.
Therefore time required to do 16 units= 16/6=2 (4/6) hours= 2 hours and 40 mins.

Therefore total time taken= 2 hours+ 2 hours 40 mins= 4 hours 40 mins = 4:40

E is the answer.
_________________

Life is a challenge face it.

Intern
Intern
avatar
B
Joined: 26 Dec 2016
Posts: 28
Re: New homeowners Jo and Colin are painting their basement. Working alone [#permalink]

Show Tags

New post 12 Jan 2018, 19:30
ScottTargetTestPrep wrote:
Bunuel wrote:
New homeowners Jo and Colin are painting their basement. Working alone, Jo could paint the entire basement in seven hours; working alone, Colin could paint it in six. They work together at their separate and constant rates for two hours; then Colin goes to work at his office while Jo continues to paint. How long in hours and minutes will it take for the basement to be completely painted?

A. 3:00
B. 3:30
C. 4:00
D. 4:18
E. 4:40


We are given that Jo’s rate = 1/7 and Colin’s rate = 1/6.

Since they both work together for 2 hours and Jo finishes the job, if we let x = the extra time Jo works, we know that Colin worked for 2 hours and Jo worked for (2 + x) hours. We can create the following equation to determine x:

(1/6)(2) + (1/7)(2 + x) = 1

2/6 + (2+x)/7 = 1

Multiplying by 42, we have:

14 + 6(2 + x) = 42

14 + 12 + 6x = 42

6x = 16

x = 16/6 = 2 ⅔

So, it takes 2 + ⅔ = 4⅔ hours or 4 hours and 40 minutes to complete the entire job.

Answer: E


just wondering why you didn't simplify 2/6 into 1/3?
Re: New homeowners Jo and Colin are painting their basement. Working alone   [#permalink] 12 Jan 2018, 19:30
Display posts from previous: Sort by

New homeowners Jo and Colin are painting their basement. Working alone

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.