ktrout2020 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

Source: Kaplan
Answer: D

One 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 rooms

Let 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 = 3

Anne'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 = 4

So, we have a system of two equations:
A + B = 3
2A + B = 4

When 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