BTGModeratorVI wrote: ↑

Sun Jul 19, 2020 1:52 pm

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

Answer: B
Source: Manhattan prep

Audrey can complete a certain job in 4 hours, while Ferris can do the same job in 3 hours.
So, Audrey's RATE = 1/4 of the job per hour
And Ferris' RATE = 1/3 of the job per hour

Audrey and Ferris worked together on the job and completed it in 2 hours, but while Audrey worked this entire time, Ferris worked for some of the time and took 3 breaks of equal length.
Since Audrey works for the entire 2 hours, let's determine how much work she does.
At a rate of 1/4 of the job per hour, Audrey can complete 1/2 of the job in TWO hours.

This means Ferris must have completed the other 1/2 of the job

Time = output/rate
So, Ferris' work time = (1/2)/(1/3) = 3/2 hours = 90 MINUTES

So, at his normal rate of work, Ferris can complete his half of the job in 90 MINUTES, which meanshe rested for the other 30 minutes.


How many minutes long was each of Ferris's break?
Ferris took 3 breaks of equal length
If he rested for a TOTAL of 30 minutes, each break was 10 minutes long.

Answer: B

Cheers,
Brent