MGMAT Rates Problem: Victors Job

[Levent-g]

Hi,
refering to MGMAT Word Translations, Page 177, Question 5.

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?

Official Solution: 60 Days

My result is 80 days and goes as following:
1) He worked half of 144 Days with and w/o supervision.
2) 72 Days with supervision in which he worked 3 days faster for each job. Hence he did 3 times as many jobs as w/o supervision. This is similar to (3*72) 216 days w/o supervision.
3) 72 Days + 216 Days = 288 Days for 36 Jobs
4) 1 Job = 288/36 Days
5) 10 Jobs = (288/36)*10 = 80 Days

Can you please check?

Thanks

Thanks

[hiteshwd]

Sure Levent

3 days faster does not mean that its is 3 times faster. Here's a simple method below to solve the Q.

Given: 144 days worked, half (72) under supervision and half (72) without, with supervision the work is completed in 3 less days

Sol: If x is the rate of work without supervision, i.e. amount of work done in 1 day without supervision= 1/x of a job

Therefore, amount of work done in 1 day with supervision= 1/(x-3) of a job

We know that, ( 72/x ) + (72/ (x-3) ) = 36

=> x = 1, 6 => x = 6, as x = 1 would make x-3 negative

Now we know that amount of work without supervision in 1 day: 1/6 of a job
Amount of work without supervision in 6 day: 1/6 * 6 = 1 job
Hence, for 10 jobs, days required= 6 * 10

Let me know if you need more help or anything is unclear.

[Levent-g]

It is pretty clear. Thanks

[RonPurewal]

well done.

if the problem has answer choices, you should also be able to work backward from the choices. (if it doesn't, you could still simulate that sort of approach by just trying a random number of days per job, and seeing whether all the statements are consistent with each other.)