Working alone, Manuel finishes cleaning

[BTGmoderatorDC]

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

[DavidG@VeritasPrep]

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

[Brent@GMATPrepNow]

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

[EconomistGMATTutor]

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.

[Scott@TargetTestPrep]

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