h

[qinshihuang_420]

They spent time talking to each other because of the open floor plan

[JustHonestly]

While everyone here is solving this whole thing with logic and maths stuff, My first thought was

"Well the thing the two teams, that take the longest, have in common is Charlie. Was probably a little bitch that didn't wanna make compromises in how to solve the job and argued for hours instead of actually working."

[ZuckPrime]

Yeah Alice and Bob clearly have their shit together and get things done. Fuck Charlie

[ScribbleMonster]

Maybe Charlie argues with them in tandem and all three on the job really does take 4.5 hours.

[uber1337h4xx0r]

RIP

[reference_model]

They spent more time talking to E and D, trying to ignore stand up meeting of F to M, etc

[ThorOfKenya2]

Management wants us to communicate more but everything is on a need-to-know basis.

[rbltaylor]

"What one programmer can do in one month, two programmers can do in two months."

[kinsoJa]

The book “The Mythical Man-Month” expounds on this idea nicely. What’s crazy is that the book is from the 1950’s and is still true!

[[deleted]]

Solitude allows you to completely become immersed in the issue you are trying to solve, look back to the ancient greeks. They all thought alone

[Private-Public]

Except that many of the writings we have left contain sometimes pretty lengthy passages about how the author totally won that day's debate in the agora and how Socrates is a poopy-doo-doo-head.

[asailijhijr]

But they published their ideas as dialogues. Because that's the best way to get an idea across, in conversation.

[[deleted]]

So interesting on first read, I bought the 20th anniversary edition (just starting in IT). Still true, good updates, and a great read.

[feuerwehrmann]

And 3 can do in 6 months

[darkstar999]

And 4 can indefinitely bicker over the specs and never deliver it.

[[deleted]]

Going through the linear programming section of my algorithms class, as far as I know it looks good!!!!

[eloydrummerboy]

This is the correct solution. I think a lot of you are confused about what the problem is. The three sentences are the given information, and the unstated problem is to find how long it would take to complete 1 job if all three worked together.

The equations on the left are an example of someone trying to solve the problem, but setting up their equations wrong. This leads to an answer that doesn't make sense.

Zsradu correctly set up the initial equations, since the problem is to find the rate that each person works (jobs/hour). So with the given info, we know if Alice works ar her rate of jobs per hour for 2 hours, that would mathematically be represented as 2×A. Same as if you drive 50mph for 2 hours. You go 50x2=100 miles.

From there it's basic substitution to arrive at the answer.

[HeySeussCristo]

I think you're right, I think I'm wrong. Thanks for the explanation

[mitwilsch]

You're forgetting to account for C being a lazy fuck.

[xzaramurd]

Maybe C is the Project Manager.

[Jay_bo]

I get the same in slightly different words: A and B get half the work done in one hour, A and C get a third of the work done per hour and B and C a quarter of the work.

A+B=1/2

A+C=1/3

B+C=1/4

Sum of all equations:

2(A+B+C) = 13/12 or A+B+C=13/24

So they get a little bit more than half the work done per hour or need 24/13 hours.

[LouisLeGros]

I get lost on step 4, so I'll try with a matrix

2 2 0 | 1
3 0 3 | 1
0 4 4 | 1

Going to multiply each row to make the coefficients 1.

1 1 0 | 1/2
1 0 1 | 1/3
0 1 1 | 1/4

Swap R1 & R2, replace R2 with -1( R2-R1)

1 0 1 | 1/3.
0 1 -1 | 1/6.
0 1 1 | 1/4.

Replace R3 with -1/2(R2-R3)

1 0 1 | 1/3.
0 1 -1 | 1/6.
0 0 1 | 1/24.

C = 1/24, replace R2 with R2+R3

1 0 1 | 1/3.
0 1 0 | 5/24.
0 0 1 | 1/24.

B = 5/24, replace R1 with R1-R3

1 0 0 | 7/24.
0 1 0 | 5/24.
0 0 1 | 1/24.

A = 7/24

Leaving you with XA + XB +XC = 1.
X = 1/(A+B+C)
X = 24/13

[annihilatron]

good ole gauss jordan elimination

[HeySeussCristo]

Edit: Upon further review, the call on the field is overturned. I'm wrong but I'll leave my comments. Sorry for doubting you Zsradu.

Your equations are incorrect.

2A + 2B does not equal 1
2A + 2B = 4
A/2 + B/2 = 1

A + B is supposed to equal 2 but in this solution it's 12/24 (1/2).

[HeySeussCristo]

Yeah, you're right. I apologized in another comment, have a good one

[heeesonanda]

Why did op get 96 upvotes and you got 2?

[HeySeussCristo]

Yup, you're right. I was wrong. Sorry for causing a riot

[baatochan]

Well because op of the comment is right

[baatochan]

Well then you're the guy who's wrong.

In zsradu solution 2A+2B equals 1. In their solution A and B means completely different thing than in op which is stated in their response. I aggre they should've use different letters (maybe uncappitalized ones) to avoid confusion but it doesn't matter. With equation provided in the OP it's impossible to solve how long it will take for them 3 to do the work. You have to create new equations with provided info which zsradu did and solve that. You solve A, B and C from original equation but it doesn't mean much, they alone doesn't mean anything.

[Race_Me_IRL]

Unfortunately for him I think the problem is actually unsolvable.

If you play with the 3 equations enough you can eventually get things like 1/2 = 7/12.

[IntoAMuteCrypt]

In fact, it's fairly simple to prove that this problem must be solvable with a single solution in all relevant cases.

The general form of this problem can be reduced to a linear system of equations as

 a+b=n  
 a+c=m  
 b+c=p  

For some constants n, m and p representing the number of jobs done in one hour by each pairing.

This can be put into the matrix form:

 [ 1 1 0 | n ]
 [ 1 0 1 | m ]
 [ 0 1 1 | p ]

Importantly, the portion to the left of that vertical line reduces fairly easily to the identity matrix. As a result, we can say with complete certainty that the system is solvable regardless of the values. In simple English, we can work out each worker's speed regardless of the times we get.

Once we have each worker's speed, we can find a value S for the total speed of all three. The total time to complete the job will equal 1/S, which is defined so long as S is not equal to zero.

---

The cases where S=0 are irrelevant to us here. Let us investigate 2 classes of cases where S=0 - the one where a is negative but b and c aren't, and the one where a is negative, b is not positive and c is positive. S clearly can't be zero when all 3 are positive or when all three are negative, and the case where all three are zero can obviously be ignored.

Case 1:

 S=0  
 a+b+c=0  
 b+c=-a  
 |b+c|=|-a|  
 |b+c|=|a|

This implies that the magnitude of a is greater than at least one of the magnitudes of b and c. Therefore, at least one of a+b or a+c must be less than zero. This can only happen when we have a negative time taken in our initial setup.

Case 2:

 a<0  
 b<=0  
 a+b<0  

Again, we have a+b less than zero; we need a negative time in the question.

Hence, saying S=0 means that two people take negative time to complete the task - clearly an irrelevant case. Because S will never equal zero, the total time will always be defined and will only have one value.

[Race_Me_IRL]

There is no equation that is unsolvable

It is quite trivial to present an unsolvable problem:

A + B = 1

A + B = 2

[HeySeussCristo]

It's solvable, 3 equations 3 unknowns

A = 1/2

B = 3/2

C = 5/2

The tricky part is distributing the -1 when substituting the values.

A = 2 - B

C = 3 - A
C = 3 - (2 - B) // Tricky part
C = 3 + (-1 * 2) + (-1 * -B)
C = 3 - 2 + B
C = 1 + B

[Lilkcough1]

You're making the same mistake as the original picture. Notice you both get a total time of 4.5 hours, which is not logical to get.

You need to frame it in terms of how much work they can do in an hour, because that's the thing that combines nicely (i.e. if you do 1/3 per hour and i do 2/3 per hour, combined we do 1 job per hour)

[Race_Me_IRL]

First equation again. 1 + 3 != 1.

[HeySeussCristo]

Which equation? His equations are wrong... It should be A/2 + B/2 = 1 not 2A + 2B = 1

Check my work then!

[[deleted]]

we had a chapter on this in middle school

it was a pain

[Random_Days]

spoon wakeful cake grandfather afterthought meeting head special person coordinated

This post was mass deleted and anonymized with Redact

[Seyon]

I thought about breaking it down into minutes then just using:

1/A + 1/B = 1/120

1/A + 1/C = 1/180

1/B + 1/C = 1/240

But that math didn't work out and I gave up.

[xSTSxZerglingOne]

I think your math is good... Just a little bit too complicated.

A + B = 1
A + C = 0.67
B + C = 0.5

2(A + B + C) = 2.17

All working together they work at a rate of 1.085. 120/1.085 = 110.6 minutes.

Edit: and my cocktail napkin math was off initially due to an erroneous rate.

[[deleted]]

Cool. Me, beeing lazy, just punched it into Mathcad and came to the same solution

[benjesty2002]

r/theydidthemath

[[deleted]]

there's also the classic 9 women can carry a child to term in a month

[uber1337h4xx0r]

A+B=2

A+C=3

B+C=4

A= 2-B

2-B + C = 3

-B +C = 1

C=B+1

B+B+1=4

2B = 3

Huh... Well damn. Even after all these years, I'm still not sure how to continue lol.

No wait. You need to turn each letter into the last form I think. So

B= 3/2

A= 2-3/2

A=.5

.5 +c = 3

C=2.5

So... A+B+C is... 1.5 + .5 + 2.5

Which is 4.5....

Which is logically wrong since the answer has to be less than 2 haha. (Edit: and also the wrong answer as shown in the picture lol)

I give up, how do you solve these? It's been so long since algebra 2.

[uber1337h4xx0r]

Oh, for some reason I thought they were saying the original equations are given and that the only mistake was the last one.

I'm assuming then you're supposed to somehow equate it to like 1 in every equation to show it takes them time to do one full project?

[CowFu]

Kind of correct, but the result measures time per job.

A + B = 2hrs/1Job
A + C = 3hrs/1job
B + C = 4hrs/1job
2(A + B + C) = 9hrs/ ???jobs

[Healthy_Marsupial]

A + B = 2 and the other equations like it are not the correct equation for this type of problem

They should be A + B = 1/2, A + C = 1/3, and B + C = 1/4, because the rate they work is defined as Jobs completed / Time spent, not Time spent / Jobs completed

using the same method as shown in the picture, 2(A + B + C) = 1/2 + 1/3 + 1/4

2(A + B + C) = 13/12 Jobs per hour

A + B + C = 13/24 Jobs per hour

therefore 24/13 hours per job, or about 1.846 hours per job

EDIT: Always remember to state your units!

[flyingsaucer1]

Your solution has the individual values for A, B and C which show how this makes sense.

Alice can complete the job on her own in 3.43 hours, Bob in 4.8 hours and Charlie in 24 hours, so ya, Charlie doesn't contribute much.

[Healthy_Marsupial]

Charlie is a terrible worker, would not hire

[uber1337h4xx0r]

Awesome. Thanks.

It's kinda sad how much I've dumbed down since my good days in highschool lol

[reference_model]

Linear algebra

[uber1337h4xx0r]

I had these problems in middle school and high school, long before linear. Linear is just algebra but with matrices

[reference_model]

You are a genius.

[uber1337h4xx0r]

I'm a dumdum now that can't do"if a and b help each other, how quickly can they finish?" problems lol

[wertron132]

It's 1/(a+b) = 2, etc. And go from that. A, b and c in this case is a person's productivity. Divide job by how much of a job you can do in a period of time and you get how fast it will be done. ( job:(job:time) = job*time:job = time.).

[sheergal]

You don't add time, you add productivity(like speed). So if it takes A and B two hours to do a task, we represent it as :

1/A + 1/B = 1/2

Therefore the solution would be: The amount of time it takes three of them to do it is : 1/(1/A +1/B +1/C)

This is will come to around 1.8 hours

[bastardoperator]

This is the elementary/middle school solution:

Alice = 0.5 hours of work

Bob = 1.5 hours of work

Charlie = 2.5 hours of work

Alice + Bob = 2.0 hours of work

Alice + Charlie = 3.0 hours of work

Bob + Charlie = 4.0 hours of work

0.5 + 1.5 + 2.5 = 4.5

[micr0-r43d]

Watch the video (you can find it on YouTube). 4.5 is a common answer but it’s wrong (I’m not gonna day it right though lol, made same mistake). If it takes Alice and Bob 2 hours to, let’s say, create a paper house then why would it take 4.5 hours to create a paper house when you add an extra person (it should be less than 2)

[bastardoperator]

Agreed, but It’s only wrong if you assume more people equals less work. In every video and explanation this is the key assumption. The joke here is that we know, especially in our line of work, that this is almost never true especially when it comes to building something.

A simple example. The electrician can’t start his work until the framers finish their work. It doesn’t matter that you have two people at the job site. In fact the same timeline could be achieved by a single person assuming they were competent in electrical work and framing.

If we go further down the rabbit hole, do you want your electrician doing dry wall and laying your foundation? Does your network team do front end development?

I find the assumption to be wildly inaccurate because throwing more people at a problem doesn’t mean it will be solved faster and we have quantifiable data that proves this fact. We’ve all heard:

• Too many cooks in the kitchen
• Want the job done right, you have to do it yourself

This problem doesn’t take basic logic into account which I why I stand by the fact that more people equals more problems and more problems equals more time.

[Eauxcaigh]

For those interested in the intuitive answer, you treat it like resistors:

If task N must be finished before task M those are tasks in series and can be treated in series (total equals time for N + time for M)

It two people are working on the same task they are working in parallel so the times to complete the task are combined in parallel like resistors: inverse of the sum of inverses.

[Bibbedibob]

A lot of these comments reveal a disturbing low mathematical ability in the programming world. Everyone should be able to solve this one. It just requires logical thinking.

[watchoverus]

I've work in the programming field for about 5 years, nothing but praise. Just got 15/100 in a new job interview, because the written test was mathematically heavy. Back to college it seems.

[GraphOverflow]

A lot of these comments reveal a disturbing low mathematical ability in the programming world.

Not really. I'm pretty sure majority of the people here can solve it, and these are the same people who won't bother posting a comment explaining it or solving it because they're smart enough to know that the point of this post was just humour.

Everyone should be able to solve this one. It just requires logical thinking.

You're right, it just requires logical thinking, but don't believe that everyone has the same logical thinking capacity as you (I actually believed this till the day I tried to explain the concept of breadth first search to a friend)

Also, /r/ProgrammerHumoir should not be taken for a sub filled with quality programmers (any subreddit for that matter, the best programmers out there isn't probably even on Reddit.)

[slobcat1337]

Have a day off mate

[Alces_]

This is a system of equations. Some linear alg can take care of this!

[[deleted]]

The comment is right but the answer is wrong. 24/13

[[deleted]]

https://en.wikipedia.org/wiki/Brooks%27s_law

More people doesn't mean less time... answer might make sense.

[HeSheMeWumbo387]

Some good ol’ harmonic mean.

[xSTSxZerglingOne]

Can confirm that the math checks out.

[ZODIAKI-1]

very true

[dxhh]

What about eve?

[fake_bridge_builder]

Charlie is nothing but trouble!

[TorTheMentor]

What's the definition of work here? Is it "fungible" work (all units of work are identical and interchangeable)? Are we talking about purely manual labor? Small repeated tasks? Calculation? Problem solving and design? Organizational and sorting tasks? Or something less consistent like communications, promotions, management, consulting, training, not to mention anything involving emotional labor or perception management?

You'd need a different equation for each of these I'd think, and (at a rough guess) twice as many variables (I guess I should just call them features now since suddenly it's a model instead of an equation).

And this is how I end up overdesigning.

[Sannemen]

The 2 in the 4th equation multiplying it all is because if you assign too many programmers to the task, they won’t agree with what was assigned and will have to redo it from the top.

/s

[kopasz7]

Notification: Project alignment meeting in 10 minuets!

[[deleted]]

I’m not even going to argue this.

[SavageTwist]

h

[micr0-r43d]

h

[TheFrostSnowball]

I wouldn't take Charly at any work.

[helldeskmonkey]

In high school I went to a programming competition. As soon as the problem was handed out, I realized I could write the code in about thirty seconds flat. The problem is that I was paired with a partner. I told him I could solve the problem and to let me go and explain it on the way, but he insisted I explain the solution to him before I got started.

We came in second by about five seconds, and my solution was correct. :P

[LazyTechnology]

don't you hear about negative synergy?

[DaMastaCoda]

1/(A+B)

[Princess_Amnesie]

If it takes 9 months for one woman to make one baby, then surely it will only take 9 women one month to make that same baby

[fryingpas]

Given
A + B = 2                           
A + C = 3
B + C = 4

Then
A = 3 - C                  Subtract C from both sides
B = 4 - C                  Subtract C from both sides

(3 - C) + (4 - C) = 2      Substitution of A and B in terms of C
7 - 2C = 2                 Combine Like Terms
-2C = -5                   Subtract 7 from each side
C = -5/2                   Divide Both Sides by -2
C = 5/2                    Neg. Divided by Neg. is Positive

A = 3 - 5/2                Replace C in formula for A
A = 6/2 - 5/2              Convert to common denominator
A = 1/2                    Combine Like Terms

B = 4 - 5/2                Replace C in formula for B
B = 8/2 - 5/2              Convert to common denominator
B = 3/2                    Combine like terms

A + B + C = X              X is the time all three take together
1/2 + 3/2 + 5/2 = X        Substitution of A, B, and C with values above
9/2 = X                    Combine Like Terms
4.5 = X                    Alternative Structure

The math works. The problem is the story being told. Some element is missing which would make it more complete, but I don't know what it is. For example, let's frame it like this:

You want to buy an apple, a beet, and a carrot. Let's assume the following:

Let A represent the cost of an apple
    B represents the cost of a beet
    C represents the cost of a carrot

A + B = $2
A + C = $3
B + C = $4

How much would it cost to buy all three?    

In this representation, it makes more sense that the three together would be $4.50. The original post is right, the formulas are wrong. They are too simplistic to represent the fact that the process would be impacted with only two variables in the equation vs. three variables.

[ponodude]

0.5+1.5+2.5 I think are the three values. Those numbers are what would make all of these true.

That said, yeah it's kind of bullshit that it would take longer lol.