

dimis
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posted November 07, 2008 05:24 AM 
bonus applied by pandora on 24 Nov 2008. 

Let's talk about Maths!!!
To my opinion, the course that is the least indifferent to all students is Math. Usually, you are a great fan, or you dislike it in any form. :)
In this thread we can talk about Math and try to discover the fun that is hidden behind the books. Post problems, paradoxa, something that bugs you, something that caught your attention, anything ... Just share the fun, and others will follow!
If you post a problem, you are in charge of the discussion (as long as you know the answer).
If you participate in a problem, try to justify your sayings. That is the most interesting part. Try to avoid random guesses. Please.
I hope this is going to be a great journey! And who knows ... perhaps Math will find new supporters!
So ... LET'S TALK ABOUT MATH!!!
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The empty set


Corribus
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posted November 07, 2008 05:38 AM 


Alright, here's a fun little math problem that most people get wrong upon their first try. I used to give it to my students to encourage them to think about a problem before they attempt to solve it.
John wants to paint his dining room. He figures it will take him 3 hours to paint the room. It would take his son, James, 5 hours to paint the room. If both of them paint it, how long will it take them to finish the room?
____________
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Celfious
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posted November 07, 2008 05:42 AM 

Edited by Celfious at 09:07, 07 Nov 2008.

I am probably wrong but here I go. 2 hours?
I forgot to mention, I factored in arguing time about who paints the most and snack time
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william
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LummoxLewis

posted November 07, 2008 05:46 AM 


I might say 3 hours. I'm probably wrong though. Even though I suck at maths, I might as well have a go at some of these. I might even improve my maths skill.
____________
~Ticking away the moments that
make up a dull day, Fritter and
waste the hours in an offhand
way~


TitaniumAlloy
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posted November 07, 2008 05:49 AM 


I would say 1.875 hours but I feel like I'm missing something
edit:
my conjecture
that if John can paint 1/3 of a room in 1 hour, and James can paint 1/5 of it, then together they can paint 8/15th of it in the 1 hour.
Hence it will take them 15/8 hours to paint the whole thing = 1.875 hours..
I had a maths exam on monday and one today, each 1 hour, and I have my final two on monday and tuesday, each 2 hours.
There are 3 maths courses available at my school. The easiest one, Further, is like statistics and some simple trig.
Then there is Methods, which is easy as well with some average calculus, circular functions, probability, related rates etc. I do this one.
Then there is Specialist, which is the hardest one, with more advanced calculus, circular functions, vectors, complex numbers, coordinate geometry, vector calculus, kinematics, population growth, related rates etc. I do this one as well.
Each has 2 exams, hence I have four exams.
Uh, yeah, that's pretty much it.
So by tuesday I will be done with maths forever I'll never have to write another number again.... oh wait
lol nah I actually don't mind it.
I have a problem that was on my maths exam on monday which I overthought and made a stupid mistake, when the answer is actually very simple so that when I showed it to my little brother he knew the answer


dimis
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posted November 07, 2008 06:09 AM 

Edited by dimis at 06:12, 07 Nov 2008.

I edited my first post.
Guessing is good as long as it is justified... Don't try to be superstitious with numbers, or at least try to prove your "conjecture".
You might feel happy if you guess right, but I am sure you 'll feel happier if you justify the solution! This is tested and works.
Whoever posts a problem is in charge of the discussion. If he/she fails to show up for a day or two and there are no more participants, I will try to take in charge.
So, Corribus, you are in charge, and thanks for participating.
____________
The empty set


Binabik
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posted November 07, 2008 07:47 AM 


Well, having been almost 30 years since I took a math class, Corribus' problem is about the level I need for review.
I come up with the same answer as TA
John paints at the rate of 1/3 room per hour and James paints at 1/5 room per hour.
T = total time to paint
Solve for T
T/3 + T/5 = 1
T(1/3+1/5) = 1
T = 1/(1/3+1/5) = 1.875
To check my answer
John paints 1.875 * (1/3) = 62.5% of the room
James paints 1.875 * (1/5) = 37.5% of the room
Last time I checked 62.5+37.5=100
To further check my answer
62.5/37.5 = 5/3

@William Even if you aren't good at math, you can still check your answer simply by thinking about it and asking yourself "Does your answer make sense?" John can paint the room in 3 hours. So you know that if someone helps him, it wil take less than 3 hours.
Doing a quick check like that can eliminate a lot of wrong answers and common errors like the decimal place being off, inverted numbers, etc.

@Celfious Did you average John and James then divide by 2?
Maybe that should be the next problem. Why can't you average the two and divide by 2? Give a text answer, not a numerical answer.


Celfious
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posted November 07, 2008 08:04 AM 


I don't remember how I got my answer but I'm almost positive its wrong anyways lol.
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dimis
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posted November 07, 2008 08:26 AM 

Edited by dimis at 08:33, 07 Nov 2008.

It's interesting because I had another approach. Well, it can't be that different, but anyway..
Let's say w is the amount of work for the entire room.
Then for the first guy we have:
w = 3 * x
and for the second guy we have:
w = 5 * y
where x, and y above represent the amount of work per hour by each of the guys. What I want now is to express w in terms of (x+y). Since this is not direct from the equations I multiply the first one by 5 and the other one by 3, i.e.:
5 * w = 15 * x
3 * w = 15 * y
Adding them I get:
8 * w = 15 * (x + y)
Now I solve for w:
w = 15/8 * (x + y)
So, 15/8 hours for me too.
____________
The empty set


JollyJoker
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posted November 07, 2008 08:51 AM 


Same than TA. 15/8 hours.
Here's a problem I found fascinating for an altogether different reason (and if you don't know the solution, but find it, you'll know why):
Imagine four points like the corners of a square:
. .
. .
Connect the four points, starting with one point, ending at the SAME point, with THREE connected straight lines. Lines may intersect.


TitaniumAlloy
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posted November 07, 2008 08:58 AM 


hmm I think I might have seen this one (or similar) before but I can't figure it out.
Ima go think and come back


dimis
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posted November 07, 2008 09:05 AM 


I know it's tempting for everyone to write down interesting problems (2 proposed so far after Corribus). But let's try to keep some pace, otherwise it will be a mess. And besides, by doing so, we give an opportunity to other people in different timezones to have the same fun. So, my suggestion is, wait for Corribus, or give this problem onefull day of life.
Best
____________
The empty set


Binabik
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posted November 07, 2008 09:25 AM 

Edited by Binabik at 09:29, 07 Nov 2008.

I see the point of not having everyone posting new questions all at once. But waiting for the original poster to "grade" the answers and give the goahead to move on might kill the thread.
Also, my question was really the same question. Just further discussion of it really.
And Dimis, that's the strangest solultion to that problem from my point of view. I would have never considered doing it that way. That is so strange to my eyes that I wonder if there is actually a difference in the approach to this type of problem taught in different countries. That wouldn't surprise me since math is taught differently in different parts of the US. And it's also changed quite a bit since when I went to school.
edit: red herring and midpoint of hypotenuse (couldn't resist)
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JollyJoker
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posted November 07, 2008 09:35 AM 


Quote:
Maybe that should be the next problem. Why can't you average the two and divide by 2? Give a text answer, not a numerical answer.
Well, the average can actually be the right answer, and here's why:
With John and James doing their work SEPARATE from each other they will need 3 and 5 hours, respectively. However, if they are working TOGETHER in the same room, there will be father/son synergy, which means, John, will spend some time showing James how to save time, how to work more efficient and so on, and correct a couple mistakes, which will mean, that John will take MORE time to finish. James will learn and continually work faster, so it actually averages out: John will take actually more time than 3 hours, while his son will need less time  in the end, they will finish in 2 hours then instead of 1.875 hours.
Another way to argue would be that two equally fast people will never manage something in half the time one would need, due to time loss for chatting, for having to share the same paint vet or the same ladder and so on.
So I actually change my solution. 1.875 is the ROBOT solution. The human solution is at least 2.


dimis
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posted November 07, 2008 09:40 AM 


Quote: I see the point of not having everyone posting new questions all at once. But waiting for the original poster to "grade" the answers and give the goahead to move on might kill the thread.
The sentence didn't end there. I proposed a maximum of 1day's life for the problem. And I don't think that the thread will be killed that easily. It is about math ...
Quote: Also, my question was really the same question. Just further discussion of it really.
I agree. Sorry for what I said.
Regarding my solution, I don't know either... That was the first and most natural thing that crossed my mind. That's why I wrote down some words too. I am sure though that I would have solved differently this kind of problem if I were younger than 15. After that age probably the exercises at school are closer to this last approach I guess. I don't know...
And I hate passingby robots that steal the paint!
____________
The empty set


william
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posted November 07, 2008 09:48 AM 


Binabik, my way of working would be that if the other person was to paint slower (5 hours) and the main guy paints in 3 hours, than it might kinda cancel each other out and might be the same since if the other guy is slower than he might not make a difference with the time they take to paint. I'm completely wrong though and I know that but meh. I guess this is the reason why I failed Maths and decided to drop it.
____________
~Ticking away the moments that
make up a dull day, Fritter and
waste the hours in an offhand
way~


Celfious
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posted November 07, 2008 10:01 AM 


lol I think I already edited my post to ensure I am right, I factored in arguing about whos right and whos wrong, and snack time lol..
But thats not true math but its the only math I know.
____________


dimis
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posted November 07, 2008 10:02 AM 


To criticize a bit and support my path to solution:
I don't like the method of reducing something to "1" which in a sense both of you are following. That's why my equations try to capture exactly what was in the sentences of Corribus. Nothing more, nothing less, and trying not to change the meaning of the sentence.
I guess it is direct bruteforce approach and treating equations like telling "stories"...
____________
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Celfious
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posted November 07, 2008 10:06 AM 


I cut them both in half.. 3=1.5 and 5 = 2.5
Added them together
4
then divided by 2
2 hours
I know I am wrong lol
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Binabik
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posted November 07, 2008 10:12 AM 


Dimis, it's not "reducing" it to 1. There is 1 room. If there were 2 rooms I would have use 2.
I answered the questions:
How fast do they paint?
How much do they have to paint?
I don't mean for this to be argumentative, just explaing my approach.
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