Work Units: Newsletter Challenge (10/03/06)

On the surface of it looks like he worked for 18 days and did not show for 12 days, receiving 36 units and paid out 36 units.

But, this is too easy for a Newsletter Challenge! So where is the catch?

I agree with your sums - I can't see the catch either!

I agree as well. And I'm not concerned with the catch; I just want to know where I can find a contractor like this.

I don't think you want this person because he/she worked for 11 days and let you sweat out for next 18 days before the work is finished!

Actually Jorrie, we all know that no union laborer 'expects' to work on weekends unless he's getting paid 4 units, and since that wasn't part of the deal... ;)
On average, any span of 30 days is going to have about 8-1/3 weekend days on which the guy is not only NOT going to work, but also NOT expect to pay the owner for not working since those are not "work days."
So - he's really going to get the job done in 13 work days, with an "average" of 8-2/3 days that he pays the owner to take off; say...8 days fishing, and a couple of Fridays that he takes off a few hours early to head for the tailgate party...
2x=3y
x+y=30-(average of either 8 or 9 weekend days ~8.33)

The catch is that he must return some of the units he recieves. Now try again.

well... I think the catch is this... ummm...... it being too easy?

I think I have to forfeit 3 units myself, Ive got no work done today, while I pondered this puzzle. I see no errors

but more information may be required,

Scheduled time off is not mentioned

Is he finished yet?

I think it is a 7th grade "homework question" cleverly disguised as a challenge, knowing the challenges will always be answered by you geniouses.

And now for something completely different, a man with...no safety program.

http://www.lateralscience.co.uk/edison/index.html

I guess one could assume that for every day he worked, the home owner received 2 units worth of work. So if the home owner broke even, the contractor must have worked every day, or at least until the job was done. If the contractor had skipped some days the home owner would have been ahead.

OK

WE don't know how many days he actually worked. we only know that attended the sight for 18 days

The question was how many days did he ACTUALLY work

States he's paid for days worked - I think he worked 18 days

I'm a contractor,

Trust me when I say, I paid people that don't actually do any work. They find places to hide

2 out of the last 2 challenges and i feel i have a 'right' answer... this is getting too easy. why was it 'dumbed' down? not enough smart people to answer correct and feel good about themselves. i preferred not knowing the answer, it gave me something to look forward to and i would feel as though i actually learnt something when the right answer was published.

Only one solution here: send in a better challenge!

18 DAYS

I too got 18 days

18 days

If you assume weekends then there are only 20 days to work with and the number of days worked would be 12 and not worked 8.

Good try, but the reason it cannot be 12 and 8 is that would require 10 weekend days in a single 30-day period, which you cannot get. That is the reason for the 13th "working day" in the solution mentioned above, and the reasoning behind choosing an approximate "average" number of weekend days for a typical 30-day month as 8.33, since some months there would be 8 weekend days, and in others there would be 9, depending on which day of the week you begin your 30 day period...

I think the catch is we all tend to overthink everything when the simplest answer is usually the best one. Concensus seems to be the man 'worked' 18 days, basic algebra: 2x-3(30-x)=0.

I agree it was too simple. Call it a vacation day. Now let's get back to the real challenges like getting the kids to eat their vegetables.

"Prohibiting irrelevant assumptions in a given theory, is justified by the fact that all assumptions introduce possibilities for error. If an assumption does not improve the accuracy of a theory, its only effect is to make the theory more error-prone, and since error is undesirable, unnecessary assumptions should be avoided."
...bandaid...

Are we assuming too much? What other factors in the contract were specified? If the discussion is on a Friday and no weekends are involved in the calculations then we negate 10 days just for rest days. Now he only worked 12 days and went fishing (or some other relaxing time off), for 8 out of a possible twenty day work period!

That was fun to do a little system of equations (the 7th grade math someone mentioned...how I wish that more American 7th graders were doing algebra, but unfortunately most will never be adequately exposed to this math level. If you ever have the chance, please volunteer to help with schools. Share your talent!) Ok enough soapboxing. When you solve the system x+y=30 and 2x-3y=0, there are two answers: 18 days and 10 days, but only 18 days checks out through the equations.

He worked 18 days.

The 18 day answer assumes that the work done has no value. By negotiation a days work was worth two units of pay (cash). The question states that the buyer paid out as much as he received. There are two things the buyer could receive: work and cash. The question does not say the buyer got the work for free, it said he broke even. Based on this argument, one can only say that the worker worked daily until the job was done or 30 days had passed.

Does this say something about engineers? That they place no value on time spent working. I don't think a profession, where the customer is charged by the hour, would consider time spent working as valueless -- i.e. a Lawyer.

This is a simple junior High linear algebra problems: two equations with two unknowns. The guy works 18 days and loafs 12 days.

or one equation and one unknown 2(x) = 3(30-x) depending on how you look at it.

18 Days!

Let X be the number of days he worked and Y be the number of days he didn't work.

Then 2X=3Y---------------(a)

and X + Y=30

So Y=30-X---------------(b)

Substituting (b) in (a), we get

2X=3(30-X)

=90-3X

Rearranging,

5X=90

So X=18 and Y=12

Cross checking, 2 times 18 equals 3 times 12.

QED.

Regards

George

Let X be the number of days he worked and Y be the number of days he didn't work.

Then 2X-3Y=X (a)

and X + Y=30 (b)

So Y=7.5 X=22.5

He actually worked 22.5 days.

Sorry, but the money to be paid must equal the money refunded, so your equation (a) should be:

2X=3Y, or 2X-3Y=0.

This will give the result most of the others got - 18 days worked, 12 days off.

The contractor was either rather bad at mathematics (which would have made him a lousy contractor) or really dumb for agreeing to be paid 2/3s of what he must forfeit for not working, for everyday he worked.

So, to forfeit the same amount as he earned, he would have worked 2/3s of the 30 days, ie, 18 days.

Everyone is thing that the contractor is working 7 days a week if you work it as 5 days a week he worked 12 days and had 8 days did not show up for the job and there where 10 days of weekends.

I agree with you guys: 2x-3(30-x)=0

enough of this.... check out the post on the first page with the link to edison. it is pretty interesting..

ok here it is again:

http://www.lateralscience.co.uk/edison/index.html

using simultaneous linear equations, we easily conclude that work was done on 18 days .

cheers-

milind chitale

singapore

Perhaps the trick lies in the weekends. It is unlikely that the contractor works on Saturdays and Sundays. If Day 1 were a Monday (logically), there would be 4 weekends or 8 weekend holidays over a period of 30 days. In that case, there were only 22 working days. Calculation yields number of days he worked as 13.4. Not good enough ! If one assumes that Day 1 is a Saturday, then there are 5 weekends ie. only 20 working days. In that case, the guy worked his guts out for 12 days and goofed off for 8 days, earning nothing in the process. Perhaps he needs some brushing up on his math skills. T D Toontant, Dubai

18 days

18

The answer is 0 he never showed up at all. He went to a bar got drunk, met a girl and moved to Florida with her. I've never seen him again. It's so hard to find good help these days!

Yep,

answer is: Worked days 18, Non-worked days 12.

a simple 2 linear equation with 2 variables is just too simple for the challenge¡¡

18days worked=36 units

12days not=36units

18+12=30 days

36-36=0

The solution can be found mathematically as follows:

WD: work days

OD: Off Days

Total work days: WD + OD = 30 (Eq.1)

Units Paid: 3*WD = 2*OD (Eq.2)

Solved equations 1&2 simultaneously gives:

WD = 18 days

OD = 12 days

Answer: He must work 18 days out of 30 working days to have the same received & paid units.

The simple and obvious answer is 18 days worked, 12 not-worked. So 18 minus 12 is 6 days. He only net'd 6 work days in a 30 day period. But, if you consider work and payment tied together he worked 0 days.

Three answers to this question, based upon different viewpoints= 18 or 6 or 0 . take your pick!

2x-3y=0

x+y=30

2x=3y

y=2x/3

x+2x/3=30

3x+2x=90

5x=90

x=18

No-one says the guy worked for a month. He could have taken 2 days off after accepting the job and then worked for 3. Apparently I only do my books once a month.

The answer is 18 days.

The problem sets up as follows:

x= days worked

y= days not worked

So: 2x-3y=0 (where y=30 days - x)

then: 2x- 3(30-x) =0; this solves to x=18

actual working days = 12 days

You have a project around the house that never seems to get done (sound familiar?). So you decide to forego the work yourself and hire a contractor. The person you hire is a bit strange and agrees to be paid 2 units for every day that he works, but will forfeit 3 units for every day that he does not work. (You agree to this arrangement, thinking it will be incentive for him to finish the project in a timely manner.) At the end of 30 days, he finds that he has paid out exactly as much as he has received. (Pretty good deal for you!) How many days did he actually work?

Your Message:12 dyas of actual work done

If the contractor works for 3 days, he gets paid 3 x 2 = 6 units. If he does not work for 2 days, he pays back 2 x 3 =6 units. So for every 5 days he works this way (3 days on, 2 days off) you get the work free. 5 days x 6 = 30 days, so he worked for 3 x 6 = 18 days, and did not work for 2 x 6 = 12 days.

I have a dim recollection of things called LCMs (Lowest Common Multiples) from my early school maths being involved in this. Must have learnt something from them!

"agrees to be paid 2 units for every day that he works, but will forfeit 3 units for every day that he does not work"

Seems like 18 days IF you assume the pool of units is unlimited. What is the catch?

Working ONLY with the units he receives the minimum days worked is 3 (receives 3x2 = 6 units), then does not work the next 2 days (forfeits 2x3 = 6 units). If he then never returns he has paid out exactly what he received, and since the pool of units is gone he does not "owe' any more units.

The work may have been free, but I would not want to be the homeowner left with the partially completed mess!
Jim P

Looks too easy to be true. In that case answer would be of course 18.

But it gets funny if you start considering that saturday and sunday are not working days. Depending on which day the 30 day (calendar) period started, you'd get 20 theoretical working days (if period starts on saturday); 22 if starting on monday or thursday; and 21 for the other days.

With these restrictions, add that we count in full days, the outcome would be that he worked 12 days and that his '30 day period' started counting on a saturday. (All other combinations don't generate an integer as result). Formula : days worked = (3xtheoretical working days)/5.

Simpelest answer could be of course 0 days, he didn't take the job!

Have fun!

I figured this out at 18 and 12 ..... and I am not even an engineer!

he worked for 18 days n not worked for 12 days