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Intern  B
Joined: 28 Dec 2010
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Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3 hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

a) 5
b) 10
c) 15
d) 20
e) 25

In 2 hours Audrey completed 2/4=1/2 of the job, so the remaining one half was completed by Ferris in 2 hours with 3 breaks of equal length.

Now, to complete the half of the job Ferris needs 1.5 hours, or 90 minutes. Ferris's schedule according to the stem was:
work-break-work-break-work-break-work.
So, the 3 breaks took 120-90=30 minutes, which means that each break was 30/3=10 minutes long.

Hope it's clear.
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

a) 5
b) 10
c) 15
d) 20
e) 25

Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12

Collective work Time = 12/7 = 1.7 Hrs

Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 3 breaks
=.3/3=.1 hrs = 10 m

so Answer is B) 10 mins
Director  S
Joined: 17 Dec 2012
Posts: 623
Location: India
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

a) 5
b) 10
c) 15
d) 20
e) 25

1. In 2 hours Audrey would have completed 1/2 of the job as he takes 4 hours to complete the job
2. Ferris completed the remaining half in those 2 hours
3. But Ferris would normally complete 1/2 of the job in 3/2 = 1.5 hours
4. So Ferris totally took break for 30 min and since he took 3 breaks of equal length , each break was 10 min long.
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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rrsnathan wrote:
gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

a) 5
b) 10
c) 15
d) 20
e) 25

Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12

Collective work Time = 12/7 = 1.7 Hrs

Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 3 breaks
=.3/3=.1 hrs = 10 m

so Answer is B) 10 mins

Portion Highlighted in red doesn't look to be correct..

1.7 hrs means 1 hr 42 minutes
total Time taken 120 minutes
So break size will be 6 minutes which is not even the answer...

0.3 Hr will be 18 minutes or 0.1 hr will be 6 minutes

Hi Bunuel,

Why can't we get answer by this method???
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Joined: 17 Dec 2012
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Location: India
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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3
mridulparashar1 wrote:
rrsnathan wrote:
gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

a) 5
b) 10
c) 15
d) 20
e) 25

Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12

Collective work Time = 12/7 = 1.7 Hrs

Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 3 breaks
=.3/3=.1 hrs = 10 m

so Answer is B) 10 mins

Portion Highlighted in red doesn't look to be correct..

1.7 hrs means 1 hr 42 minutes
total Time taken 120 minutes
So break size will be 6 minutes which is not even the answer...

0.3 Hr will be 18 minutes or 0.1 hr will be 6 minutes

Hi Bunuel,

Why can't we get answer by this method???

You would not get the answer by the above method because only Ferris took the break, So you need to get the breaks only from the time Ferris totally took. But above, you are instead calculating the time taken with both working and then trying to find the break time. But since Ferris took some breaks you would not get the answer this way.
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Manager  Joined: 25 Oct 2013
Posts: 141
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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1
Audrey works 4 hrs to get the job done. So in 2 hours Audrey completed 1/2 the work. To complete the remaining half Ferris needs only 1.5 hours that is 90 mins. However he took 3 breaks and finished the work in 2 hrs. Therefore Ferris took a break of 120 min - 90 mins = 30 mins spread across 3 equal sessions. So each break is 30/3 = 10 mins.
Manager  Joined: 20 Dec 2013
Posts: 222
Location: India
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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1
Option B.
Let the units of work be 12 units(LCM of 3,4)
A's rate=3u/hr
B's rate=4u/hr
A works continuously for 3 hrs,So A will complete 6u of work.
The remaining will be completed by F in 2 hrs.
Now F' rate without break is 8u in 2 hrs.But actually he did only 6u in 2 hrs.
So the time he take to complete 2u=Time he spent on breaks.
60 min=4u
So 15 min=1u
And 30 min=2 u
Divide by 3 we get 10.
Manager  Joined: 20 Dec 2013
Posts: 222
Location: India
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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Approach #2:A took 4 hrs. to complete the work.
So in 2 hrs. he'll do half the work and rest will be done by F.
No F does whole work in 3 hrs.So he'll do half the work in 1.5 hrs.
But he worked for 2 hrs.
So 0.5 hrs is his break time.Divide by 3 we get 10.
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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2
rrsnathan wrote:
gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

a) 5
b) 10
c) 15
d) 20
e) 25

Audery and Ferris collective Work rate:
1/4 + 1/3 = 7/12

Collective work Time = 12/7 = 1.7 Hrs

Job Was actually done in = 2 (Includes breaks)
Breaks = Actual time taken - Collective work time
= 2 - 1.7
= .3 Hrs = 1/2
so ferrais took 3 breaks
=.3/3=.1 hrs = 10 m

so Answer is B) 10 mins

Portion Highlighted in red doesn't look to be correct..

1.7 hrs means 1 hr 42 minutes
total Time taken 120 minutes
So break size will be 6 minutes which is not even the answer...

0.3 Hr will be 18 minutes or 0.1 hr will be 6 minutes

Hi Bunuel,

Why can't we get answer by this method???[/quote]

You would not get the answer by the above method because only Ferris took the break, So you need to get the breaks only from the time Ferris totally took. But above, you are instead calculating the time taken with both working and then trying to find the break time. But since Ferris took some breaks you would not get the answer this way

Combined rate, if calculated, comes up = 7/12, so time taken = 12/7

However, given that both combined took time of 2 hours, so the given information supersedes the calculated part, hence this approach cannot be taken
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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4
........................ Rate ................. Time .................. Work

Audrey ............. $$\frac{1}{4}$$ ..................... 4 ..................... 1

Ferris ............... $$\frac{1}{3}$$ ..................... 3 ...................... 1

Combined .................................... 2 ........................... This is the given information inclusive of 3 breaks

Audrey worked nonstop for 2 hours, work done $$= \frac{1}{4} * 2 = \frac{1}{2}$$

Work left over for Ferris $$= 1 - \frac{1}{2} = \frac{1}{2}$$

Time required by Ferris$$= \frac{1}{2} * 3 = 1.5$$

Break taken by Ferris = 2 - 1.5 = 0.5 = 30 Minutes

Each break = 10 Minutes

Intern  Joined: 07 Jun 2013
Posts: 9
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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Let Ferris takes x hrs including break to complete the work alone. Given Audrey alone takes 2 hrs and Ferris alone takes 3 hrs, and together they takes 2 hrs to complete the work.
So, 1/2+1/x=1/2.
Solving x=4 hrs.
Implies in total 4 hours of work time, Ferris works for 3 hours and takes 1 hr break. Therefore, in total 2 hours of work time, he will take 30 minutes of break. There are 3 equal breaks, so each break will be equal to 10 mins.

B
Manager  Joined: 22 Aug 2014
Posts: 134
Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25

WHAT IS THE PROBLEM IN BELOW METHOD:

y=total time of 3 breaks

1/4+1/(3+y)=1/2
y=1 hours and thus each break 20 mins long
What I am doing wrong? Current Student S
Joined: 13 Nov 2014
Posts: 107
GMAT 1: 740 Q50 V40 Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25

I did this a completely different way that may not be optimal.

so A does a rate of 1/4 per hour and F does a rate of 1/3 per hour. Convert those to 4/12 (for F) and 3/12 (for A).

We know that A worked for the full 2 hours so A did 6/12 of the job, which means that F completed 6/12 of the job.

If F took no breaks, he would have completed 8/12, but we only need 6/12 so we have a difference of 2/12. So F need take breaks for a total of 1/4 of the total time.
1/4 of two hours is 30 mins and he took 3 breaks (30/3=10). Each break = 10 mins

B
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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2
Presenting the detailed solution

Given
We are told about the time taken by Audrey and Ferris to do a work(let's say W) i.e. 4 hours and 3 hours respectively. We are also told that both of them working together take 2 hours to complete the job. However during these 2 hours, Ferris took 3 breaks of equal time intervals whereas Audrey worked for the full 2 hours. We are asked to find the time taken by Ferris for each break.

Approach
We know that Work = Rate * Time. Since we are given the time taken by both Audrey & Ferris to do a particular work we can find out their respective rates in terms of work done i.e. W
For the situation when both of them are working together, we know the following:

a. Amount of work to be done i.e. W
b. Rate of work done by Audrey & Ferris in terms of W
c. Time for which Audrey worked

We can use the above information and the time rate equation to find out the time for which Ferris worked which can be used to calculate the time taken by Ferris for each break.

Working Out
Let the amount of work done be W.

Rate at which Audrey works
$$W = Ra * 4$$ i.e. $$Ra = \frac{W}{4}$$

Rate at which Ferris works
Similarly $$Rb = \frac{W}{3}$$

Both Audrey & Ferris working together
Let's assume the time for which Ferris worked be t.

$$W = Ra * 2 + Rb * t$$

$$W = \frac{W}{4} * 2 + \frac{W}{3} * t$$

$$t = 1.5$$ hours. Since Ferris worked for 1.5 hours, he took a total break of ( 2 - 1.5) hours = 30 minutes. Since he took 3 equal breaks his each break length = $$\frac{30}{3} = 10$$ minutes.

Hope this helps Regards
Harsh
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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Wofford09 wrote:
gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25

I did this a completely different way that may not be optimal.

so A does a rate of 1/4 per hour and F does a rate of 1/3 per hour. Convert those to 4/12 (for F) and 3/12 (for A).

We know that A worked for the full 2 hours so A did 6/12 of the job, which means that F completed 6/12 of the job.

If F took no breaks, he would have completed 8/12, but we only need 6/12 so we have a difference of 2/12. So F need take breaks for a total of 1/4 of the total time.
1/4 of two hours is 30 mins and he took 3 breaks (30/3=10). Each break = 10 mins

B

Perfect logic.
I would just explain this "So F need take breaks for a total of 1/4 of the total time."
Since his rate of work is 4/12 and he does 6/12 of the work, time taken = Work/Rate = (6/12)/(4/12) = 1.5 hrs.
So he took a break for half an hour i.e. 30 mins and then proceed.
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25

if ferris takes no breaks, then in 2 hours
he and audrey can complete 2(1/4+1/3), or 7/6 of the job
thus, ferris' total break time accounts for 1/6 of the job
if ferris can do entire job in 3 hours, then he can do 1/6 of job in 1/2 hour
1/2 hour=30 minutes
30/3=10 minutes per break
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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1/4+1/3=7/12 is combined rate

(7/12)*2=14/12 is a work without break

14/12-12/12=2/12 is a work not done due to the breaks

(2/12):(1/3)=1/2hours dedicated to 3 breaks, so one break is 10 min

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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25

Let the total work be 12

Efficiency of Audrey = 3
Efficiency of Ferris = 4

Let total break of Ferris be x Hour

SO, 3*2 + 4 ( x - 2 ) = 12

Or, 6 + 4x - 8 = 12

Or, 4x = 24

Or, x = 6

Thus each of Ferris break was 6/60 hrs = 10 minutes...

Answer will be (B) 10 minutes...
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Re: Audrey 4 hours to complete a certain job. Ferris can do the  [#permalink]

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gary391 wrote:
Audrey 4 hours to complete a certain job. Ferris can do the same job in 3hours. Audrey and Ferris decided to collaborate on the job, working at their respective rates. While Audrey worked continuously, Ferris took 3 breaks of equal length. If the two completed the job together in 2 hours, how many minutes long was each of Ferris’ breaks ?

A. 5
B. 10
C. 15
D. 20
E. 25

The rate of Audrey is 1/4 and the rate of Ferris is 1/3.

If we let each break of Ferris equal x, his time worked is 2 - 3x ad Audrey’s time is 2. We can create the following equation and solve for x:

(1/4)(2) + (1/3)(2 - 3x) = 1

Multiplying by 12 we have:

6 + 4(2 - 3x) = 12

8 - 12x = 6

2 = 12x

1/6 = x

So each break was 1/6 x 60 = 10 minutes long.
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