Working alone, Manuel finishes cleaning half the house in

AAPL 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

Answer: E

Cheers,
Brent

Hi All,

We're told that working alone, Manuel finishes cleaning HALF the house in a THIRD of the time it takes Nick to clean the entire house alone and that Manuel alone cleans the entire house in 6 hours. We're asked for the number of hours it would take Nick and Manuel to clean the entire house if they work together. This question can be solved with the Work Formula:

(A)(B)/(A+B) where A and B are the individual times that it takes to complete the task

We know that Manuel can clean the ENTIRE house in 6 hours. Thus, it would take Manuel 3 hours to clean HALF the house...which means that it would take Nick 9 hours to clean the ENTIRE house.

With those 2 values (6 hours and 9 hours), it would take (6)(9)/(6+9) = 54/15 = 3 9/15 = 3.6 hours to clean the house together.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

AAPL 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

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