Working alone, Manuel finishes cleaning

This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members
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

User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 am
Location: Boston, MA
Thanked: 1153 times
Followed by:128 members
GMAT Score:770

by DavidG@VeritasPrep » Fri Oct 06, 2017 5:51 am
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

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 » Fri Oct 06, 2017 7:30 am
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
Image

User avatar
GMAT Instructor
Posts: 555
Joined: Wed Oct 04, 2017 4:18 pm
Thanked: 180 times
Followed by:12 members

by EconomistGMATTutor » Fri Oct 06, 2017 8:47 am
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[/
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.

Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7222
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members
BTGmoderatorDC wrote:
Fri Oct 06, 2017 4:36 am
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
We see that Manuel’s rate is 1/6, so it takes him 3 hours to clean half the house. This means it will take Nick 9 hours to clean the entire house. Thus, Nick’s rate is 1/9.

Working together, their combined rate is 1/6 + 1/9 = 3/18 + 2/18 = 5/18, so the time it takes them to clean the entire house is 1/(5/18) = 18/5 = 3.6 hours.

Answer: E

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage