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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