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

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While working alone at their respective constant rates, Audrey took 4  [#permalink]

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New post 15 May 2019, 23:05
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E

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Question Stats:

42% (02:26) correct 58% (02:22) wrong based on 33 sessions

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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

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Re: While working alone at their respective constant rates, Audrey took 4  [#permalink]

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New post 15 May 2019, 23:38
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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
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Re: While working alone at their respective constant rates, Audrey took 4  [#permalink]

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New post 16 May 2019, 02:18
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Bunuel wrote:
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


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
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Re: While working alone at their respective constant rates, Audrey took 4  [#permalink]

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New post 19 May 2019, 19:59
Bunuel wrote:
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


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
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Re: While working alone at their respective constant rates, Audrey took 4  [#permalink]

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New post 21 May 2019, 20:56
1
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.

Bunuel wrote:
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

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Re: While working alone at their respective constant rates, Audrey took 4   [#permalink] 21 May 2019, 20:56
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