swerve 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 job = the LCM of the 3 times = 12 units.

Since Audrey's time alone = 4 hours, Audrey's rate = w/t = 12/4 = 3 units per hour.
Since Ferris's time alone = 3 hours, Ferris's rate = w/t = 12/3 = 4 units per hour.

Since Audrey works for the entire 2 hours, the work produced by Audrey = rt = 3*2 = 6 units.
Remaining work = (total job) - (Audrey's work) = 12 - 6 = 6 units.
Since Ferris's rate = 4 units per hour, the time for Ferris to produce the remaining 6 units = w/r = 6/4 = 1.5 hours.
Since Ferris works for 1.5 of the total 2 hours -- implying that his 3 breaks sum to 30 minutes -- the time for each break = 10 minutes.

The correct answer is B.

swerve 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.

Answer: B