Am stuck !! Pls help !!

This topic has expert replies
User avatar
Senior | Next Rank: 100 Posts
Posts: 49
Joined: Mon Feb 10, 2014 1:18 am
Followed by:3 members

Am stuck !! Pls help !!

by candygal79 » Wed Mar 26, 2014 8:33 pm
2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes

My workout :

1/4 +1/6 = 5/12 , am stuck after this .

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Mar 26, 2014 10:31 pm
candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
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.

Now onto the question...
Sally can paint a house in 4 hours, and John can paint the same house in 6 hours
So, according to green rule, Sally paints 1/4 of the house in 1 hour, and John paints 1/6 of the house in 1 hour
COMBINED, the fraction of the house they can paint in 1 hour = 1/4 + 1/6
= 3/12 + 2/12
= 5/12
So, they can paint 5/12 of the house in 1 hour

If they can paint 5/12 of the house in 1 hour, then according to blue rule, they can paint ENTIRE house in 12/5 hours.
12/5 hours = 2 2/5 hours
= 2 hours and a bit
= A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Mar 26, 2014 11:27 pm
candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
Alternatively, we can use a bit of logic.

Notice that John is the SLOWER painter.

John can paint the same house in 6 hours
So, if John were to work with ANOTHER painter who painted at the SAME SPEED, the two identical painters could paint the house half the time.
In other words, they could paint the house in 3 hours.

Since Sally can paint FASTER than John, then John and Sally would be able to paint the house even faster than John and an identical painter.
In other words, John and Sally would be able to paint the house in LESS than 3 hours.

Since only answer choice A is less than 3 hours, the correct answer is A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Thu Mar 27, 2014 12:24 am
Hi candygal79,

This question involves 2 people working on a job together, so it's perfect for the Work Formula:

Work = (AxB)/(A+B)

A and B represent the amount of time that it takes each person to paint the house:

A = 4 hours
B = 6 hours

Now plug in...

(4x6)/(4+6) = 24/10 hours

2.4 hours = 2 hours 24 minutes

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Mar 27, 2014 3:25 am
candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
Let the house = 12 units.
Since Sally can paint 12 units in 4 hours, Sally's rate = w/t = 12/4 = 3 units per hour.
Since John can paint 12 units in 6 hours, John's rate = w/t = 12/6 = 2 units per hour.
Combined rate for Sally and John = 3+2 = 5 units per hour.
Time for Sally and John together to paint 12 units = w/r = 12/5 hours = 2 hours, 24 minutes.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

Am stuck !! Pls help !!

by Brent@GMATPrepNow » Wed Jan 10, 2018 7:11 am
candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes
We can solve this question quickly by using a little number sense.

Sally can paint a house in 4 hours
So, if there were TWO Sallys, they'd be able to paint the house in HALF the time.
In other words, TWO Sallys could paint the house in 2 hours

John can paint the same house in 6 hours
So, if there were TWO Johns, they'd be able to paint the house in HALF the time.
In other words, TWO Johns could paint the house in 3 hours

So, the time it takes Sally and John to paint the house will be BETWEEN 2 hours and 3 hours

This allows us to eliminate B, C, D, and E

Answer: A
Brent Hanneson - Creator of GMATPrepNow.com
Image

Master | Next Rank: 500 Posts
Posts: 100
Joined: Wed Nov 29, 2017 4:38 pm
Thanked: 14 times

by GMATWisdom » Wed Jan 10, 2018 7:27 am
candygal79 wrote:2. If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes

My workout :

1/4 +1/6 = 5/12 , am stuck after this .
1/4+1/6=5/12 is ok. that means 5/12 th work is done by both in one hour, so complete work will be done in 1/(5/12)=12/5 hours which is equal to 2hours and 24 minutes.
hope no more confusion left.