Bruce and Anne can clean their house in 4 hours working toge

Question

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

A. 6
B. 7
C. 8
D. 12
E. 14

mau5 · Accepted Answer

As rates are additive,

Ra+Rb = 1/4

2*Ra+Rb = 1/3

Subtract both the equations, we have

Ra = 1/12.

D.

aceacharya · Answer

Lets suppose Anne and Bruce take A and B hrs working separately
So in 1 hour they can together finish 1/A + 1/B portion of the work which equals 1/4 (As the work is completed in 4 hours)
After anne doubles her rate of work the portion completed by the both is 1/A +2/B which is equal to 1/3 (As the work is completed in 3 hours)

Solving these 2 equations we can find B as 12 
So, D

mdbharadwaj · Answer

1/a + 1/b =1/4.--(1)

now ann's rate is doubled.
2/a+1/b = 1/3 => 1/a+1/a+1/b = 1/4 using 1/a+1/b from from (1) 1/a+1/4 = 1/3 or a =12. 
Option D

DDB1981 · Answer

Another way to look at it is:

Rate of A and B combined = Rate A + Rate B = 1job/4hrs

If A doubles and works with B, we have:

Rate A +   = 1job/3hrs

or

Rate A +1job/4hrs = 1job/3hrs

so

Rate A = 1/3 - 1/4 = 4/12 - 3/12 = 1/12 = 1job/12hrs (so basically, one job takes 12 hours)

oop-- so answer D! Hope that helps!

wolfmarc · Answer

1/A = Anna's rate; 1/B= Bruce's rate

1/A+1/B=1/4
&
2/A+1/B=1/3

Combining both equations:
1/A+(1/A+1/B)=1/3

1/A=1/3-1/4=1/12

R=W/T pick (D).

madzstar · Answer

DaNG! All you people did some complex workout all i did was 3x4= 12 FINISHED! hahahahaaa

tomluzer · Answer

I truly appreciate your answering quality. Rather having confusing and complex workout,solution must be precise and illustrative.
I agree to your answering skill.The answer is  D .

SrinathVangala · Answer

Looking at it in a different .(I don't want to work with fractions)

a = amount of work done by anne in one hour
b = amount of work done by bruce in one hour

4a + 4b = W(work)

6a + 3b = W

which implies 2a = b

which gives W = 12a

So it takes anne 12 hours to complete the work

unceldolan · Answer

work = rate * time

set up equations.

Working together, normal rate: 1(job) = (A + B) *4 => 1/4 = A+B
Working together, double speed of A: 1(job) = (2A+ B) *3 => 1/3 = 2A+B

Substract first equation from second.
1/12 = A 
This means she finishes 1(job) every 12(hours). Hence D.

BrentGMATPrepNow · Answer

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 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

Subhrajyoti · Answer

Bruce & Ann-- together complete work in 4 hrs-- rate is 1/4. Assuming Bruce rate is B and Ann rate is A
Now Ann doubles her speed thus we can say 2A+b= 1/3 -- rate. We have 2 eq-- A+B=1/3 and 2A+b=1/4, subtracting them yeilds a=1/12-- this is the work done by Ann in 1 hr, so we can say Ann completes 1/12 work in 1 hr, therefore she will complete the whole work in 12 hrs.

NicoleZR · Answer

1/a+1/b=4
1/a+1/b/2=3
Abstract both, you will find the answer B=12

D.

Posted from my mobile device

Bruce and Anne can clean their house in 4 hours working toge

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Bruce and Anne can clean their house in 4 hours working toge

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards