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
