pikachu wrote:

Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. If Anne’s speed were doubled, they could clean their house in 3 hours working at their respective rates. How many hours does it currently take Anne to clean the house on her own?

A. 6

B. 7

C. 8

D. 12

E. 14

Another approach is to

assign a NICE value to the job.

We'll choose a value that works well with the given information (4 hours and 3 hours)

So let's say the cleaning job consists of cleaning

12 roomsLet A = the number of rooms that Anne can clean in ONE hour

Let B = the number of rooms that Bruce can clean in ONE hour

Bruce and Anne can clean their house in 4 hours working together at their respective constant rates. This tells us that their COMBINED rate =

12 rooms in 4 hours = 3 rooms per ONE HOUR

In other words,

A + B = 3Anne's speed were doubled, they could clean their house in 3 hours working at their respective rates. This tells us that their NEW COMBINED rate =

12 rooms in 3 hours = 4 rooms per ONE HOUR

If we DOUBLE Anne's speed, we get 2A

So, we can write:

2A + B = 4So, we have a system of two equations:

A + B = 3

2A + B = 4When we solve the system, we get A = 1 and B = 2

If A = 1, then this means Anne can clean 1 room in ONE hour

How many hours does it currently take Anne to clean the house on her own? Time = output/rate

=

12 rooms/1 room per hour

= 12 hours

Answer: D

Cheers,

Brent

_________________

Brent Hanneson – Founder of gmatprepnow.com