guerrero wrote:Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long would it take Victor to complete 10 jobs without any supervision?
A. 34
B. 52
C. 60
D. 70
E. 92
OA c
Here's an algebraic approach.
Let u = days to complete a job when unsupervised
So, u - 3 = days to complete a job when supervised
This means that
in 1 day, Victor completes 1/u of the job when unsupervised.
Likewise, in
1 day, Victor completes 1/(u-3) of the job when supervised.
If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs.
In other words, Victor work 72 days unsupervised and 72 days supervised.
So, for the 72 unsupervised days, Victor will complete 72/u jobs
For the 72 supervised days, Victor will complete 72/(u-3) jobs
We're told that Victor completes a total of 36 jobs. So . . .
72/u + 72/(u-3) = 36
Multiply both sides by (u)(u-3) to get: 72(u-3) + 72u = 36(u)(u-3)
Expand: 72u - 216 + 72u = 36u^2 - 108u
Simplify: 36u^2 - 252u + 216 = 0
Divide both sides by 36: u^2 - 7u + 6 = 0
Factor: (u-1)(u-6) = 0
So, u = 1 or 6
If u = 1, then u-3 (the number of days to complete a job when supervised) will equal -2. This is impossible, so we can rule out u = 1.
This means that u = 6.
In other words, when unsupervised, it takes Victor 6 days to complete a job.
So, to answer the question, it will take Victor
60 days to complete 10 jobs.
Answer =
C
Cheers,
Brent
