While working alone at their respective constant rates, Audrey took 4

Question

While working alone at their respective constant rates, Audrey took 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

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

ScottTargetTestPrep · Accepted Answer

Audrey’s rate is ¼, and Ferris’ rate is ⅓. Let x be the number of minutes of each of Ferris’ breaks (notice that each of her breaks is x/60 hours long). We can create the following equation:

2(¼) + (2 - 3 * x/60)(⅓) = 1

½ + (2 - x/20)(⅓) = 1

½ + ⅔ - x/60 = 1

Multiplying the above equation by 60, we have:

30 + 40 - x = 60

x = 10

Alternate Solution:

In total, Audrey has worked for 2 hours and Ferris has worked for 2 hours minus the total time for her breaks.

Since it takes 4 hours for Audrey to complete the whole job, she completed 1/2 of the job in 2 hours; which leaves Ferris to complete the remaining 1/2.

Since Ferris can complete the whole job in 3 hours, it would have taken her 3/2 = 1.5 hours to complete half the job. Since the actual time Ferris spent working is 1.5 hours, her total time spent on breaks is 2 - 1.5 = 0.5 hours = 30 minutes. Since the brakes are equal length, each brake was 30/3 = 10 minutes long.

Answer: B

Chethan92 · Answer

Let the total work to be done = LCM(3,4) = 12
A does 3 units per hour.
F does 4 units per hour.
Together they do 7 units per hours.
In two hours they'll complete 14 units.
But the total work to be done is 12 units.
Remaining two units are the break taken by F.
F does 4 units in 1 hour.
2 units in 30 minutes.
Hence F took 10 minutes break 3 times.

B is the answer

Archit3110 · Answer

rate of A = 1/4
rate of f=1/3
total work done ;
7/12 and work done in 2 hrs 
7/12 * 2 ; 7/6
so work left ; 7/6-1 ; 1/6
this work left was completed in 3 parts ; so 1/6/1/3 ; 1/2 done per hr 
1/2 * 60 ; 30 mins or say 10 mins each 
IMO B

btrg · Answer

Lets try to solve this verbally. Audrey will do 50% of the work in 2hrs. Rest 50% of the work will be done by Ferris. But Ferris can do 50% of the work in 1.5 hrs as per question. So if he worked 2hrs and took equal breaks, then those breaks have to be of 10min each. i.e 120 min - 30(3*10) min = 1.5 hrs.

So B.

CrackverbalGMAT · Answer

In time and Work, completion of work = 1

When 2 or more people work for different time periods, then the sum of the fractions of work done by each person = 1

Work done by Audrey in 1 hour =  \frac{1}{4}

Work done by Ferris in 1 hour =  \frac{1}{3}

Fraction of work done by Audrey in 2 hours =  \frac{2}{4}  =  \frac{1}{2}

Let length of Ferris's break = x hours each

Total Length of the break = 3x hours

Amount of time worked by Ferris = 2 - 3x hours

Fraction of work done by Ferris in 2 hours =  \frac{2 - 3x}{3}

Therefore  \frac{1}{2} \space + \space \frac{2 - 3x}{3} = 1

\frac{3 \space + \space 2 \space* \space(2\space - \space 3x)}{6} = 1

3 + 4 - 6x = 6

x = \frac{1}{6}  hours = 10 minutes

Option B

Arun Kumar

TarunKumar1234 · Answer

Given, A = 4 hrs and F = 3 hrs. To complete 1 work, 1/3* (2-3T) + 1/4*2 =1 or, T = 7/6 -1 = 1/6 hrs = 10 mins So, I think B.

nkothari1997 · Answer

Let total manpower required for the work be 12 units. (LCM of 4,3)
Therefore, Audrey does 3 units of work each hour. (12 units/3 hours)
Similarly, Ferris does 4 units of work each hour.
According to the question, when they work together they take 2 hours to complete the work. 
Audrey does 6 units(3*2) of work.
Remaining work=12-6=6 units
Ferris should have finished this amount of work in 1.5 hours (6 units/4). 
But the actual time is 2 hrs. 
Therefore break interval=((2*60)-(1.5*60))/3=10 minutes

rvgmat12 · Answer

A - 3 units per hour
F- 4 units per hour

Work - 12 units

A - 6 units
F - 6 units in 2 hours

He must take 1.5 hours for 6 units. So break of .5 hour or 30 minutes

Each break is of 10 min length

bumpbot · Answer

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While working alone at their respective constant rates, Audrey took 4

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