Why do we assume all existence facts are given in math word problems?

[Amad27]

Hello,

I just had a simple question on inferences in math word problems.

Suppose you are given a

A chemical flows into a storage tank at a rate of 180 + 3t liters per minute, where t is the time in minutes and 0 <= t < 60. Find the amount of the chemical that flows into the tank during the first 20 minutes.

My question is, it doesn't say anything about the chemical flowing out of the storage tank there.

Then why do you infer that chemical DOESNT flow out of the tank?

MY THOUGHTS

Since this is after all, communication. Could it be that

You are expecting all existence facts to be given beforehand?

But then

WHY do you infer that all existence facts have been given beforehand?

Is it because that is how communication works? why?

Thank you
-Olok

 

[Prove It]

You can only solve a problem if all information is given.
Thus if all information is not given, you can not solve the problem.

A problem would only be posed if it is to be solved. Thus all necessary information must have been given.

 

[Nono713]

If you are given a school problem to solve, and there are two or more possible interpretations which lead to more or less work on your part, it is probable the teacher meant the one involving the most work. In this case, applying the above principle clearly leads to the conclusion that the storage tank is bottomless and that you must calculate the required integral.

 

[MarkFL]

I agree...if there is no information given regarding a flow out of the tank, then my interpretation would that there is none. I would assume the tank is large enough to contain all of the flow in, and compute the resulting integral or perhaps observe we have a trapezoidal area that may be computed by geometric means.

edit: We can actually ignore any flow out...the problem does not ask how much chemical is contained in the tank at some point in time, it simply asks how much has flowed in during that time. So the question of whether there is flow out or not is moot.

 

[Dethrone]

At least to me, drawing questions such as "why doesn't the chemical flow out" is tantamount to "why doesn't the chemical also evaporate". Simply put, if it's not stated in the question, it's (generally) implied that it doesn't happen. Otherwise, we'll be stuck thinking about the question forever, contemplating what else could have happened.

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Furthermore, we can infer that the chemical doesn't flow out of the tank because the question explicitly says that: A chemical flows into a storage tank.

 

[Amad27]

At least to me, drawing questions such as "why doesn't the chemical flow out" is tantamount to "why doesn't the chemical also evaporate". Simply put, if it's not stated in the question, it's (generally) implied that it doesn't happen. Otherwise, we'll be stuck thinking about the question forever, contemplating what else could have happened.

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Furthermore, we can infer that the chemical doesn't flow out of the tank because the question explicitly says that: A chemical flows into a storage tank.

Hi there,

I would like to ask you something.

What was your OWN reason why you didnt assume the chemical evaporated for example?

What was your reason for not assuming unstated items exist before I asked the question? DId you ever think about it?

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Hi,

Also, can anyone confirm this.

By experience you know that the word problem is supposed to teach you something (homework for example).

Could this be a reason?ALSO

What was your PERSONAL reason for not assuming for example no chemicals evaporating?

In general when you did word problems why did you ignore the unstated possiblities?
Was there any reason at all?

 

[Dethrone]

You're right, I did assume the chemicals evaporating a possibility. Not only that, I assumed that friction and air resistance had an impact on the chemicals, and worried that perhaps, if there was a nuclear plant nearby, that could have an unseen effect on the chemical. (I'm joking). In a more serious note, I did not assume those things because it was not stated in the question, and even IF we were to assume those facts, we would have no means to solve them. i.e the rate that the chemicals flowed out of the tank was NOT given. In other words, even if we were to assume something, if we were not given sufficient information, then it is a useless assumption. I think you should reread Prove It,Bacterius, and MarkFL's post; I don't want to re-iterate them.

 

[Amad27]

You can only solve a problem if all information is given.
Thus if all information is not given, you can not solve the problem.

A problem would only be posed if it is to be solved. Thus all necessary information must have been given.

Thank you Prove It. I think this is an excellent explanation.

Tell me one thing,

Isn't it weird why they never teach this in school? In school-mathematics they never say you should make these assumptions because the problem is to be solved.

THANKS TO ALL!

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You're right, I did assume the chemicals evaporating a possibility. Not only that, I assumed that friction and air resistance had an impact on the chemicals, and worried that perhaps, if there was a nuclear plant nearby, that could have an unseen effect on the chemical. (I'm joking). In a more serious note, I did not assume those things because it was not stated in the question, and even IF we were to assume those facts, we would have no means to solve them. i.e the rate that the chemicals flowed out of the tank was NOT given. In other words, even if we were to assume something, if we were not given sufficient information, then it is a useless assumption. I think you should reread Prove It,Bacterius, and MarkFL's post; I don't want to re-iterate them.

Thank you, all these posts helped.

A question for you. Why do you think they never teach this in school?

 

[Dethrone]

It doesn't need to be taught, it makes complete sense. For example, if you were doing an introductory calculus course on kinematics, would you assume all the factors related to air resistance and the such? No, you haven't learned it, nor does the question give you relevant data regarding the air resistance, and you're just over-thinking a basic question.

 

[Amad27]

It doesn't need to be taught, it makes complete sense. For example, if you were doing an introductory calculus course on kinematics, would you assume all the factors related to air resistance and the such? No, you haven't learned it, nor does the question give you relevant data regarding the air resistance, and you're just over-thinking a basic question.

Hi Rido12, thanks a bunch. Could it be though,

In school they teach you how to SOLVE word problems, so they never include the possibility of a hole and such/

 

[Dethrone]

Hi Rido12, thanks a bunch. Could it be though,

In school they teach you how to SOLVE word problems, so they never include the possibility of a hole and such/

Can you elaborate on what you're trying to say? They never teach you in school to "solve word problems". You simply examine what you're given and what you're trying or required to do. It's self-explanatory that you're not going to bring in concepts that require multivariable calculus in a high school physics class.

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Don't assume things that are not given in a problem. You are to assume a perfect scenario. Most problems even tell you: "please ignore air resistance" or "assume no friction". In your question, a perfect scenario is that the chemical does not corrode the material of the tank, the tank has has no holes, chemical does not leak, and the chemical does not react with the elements in the atmosphere.

 

[MarkFL]

...In school they teach you how to SOLVE word problems, so they never include the possibility of a hole and such/

Once you are ready to mathematically deal with a hole in the container, then information about the hole will be given. If no mention of a hole is made, then you are to reasonably assume then that there is no hole.

If no mention is made of a siphon, then you are to assume no siphoning is occurring. If no mention is made of evaporation, teleportation of material away by extraterrestrials, dipping away of material by your grandmother, etc., then you are to assume these things are not happening.

For a well-written problem, you will be given information about everything relevant by the author of the problem that is needed to solve the problem. :D

 

[Dethrone]

If no mention is made of a siphon, then you are to assume no siphoning is occurring. If no mention is made of evaporation, teleportation of material away by extraterrestrials, dipping away of material by your grandmother, etc., then you are to assume these things are not happening.
:D

I second this (Clapping)(Giggle)

 

[Amad27]

Can you elaborate on what you're trying to say? They never teach you in school to "solve word problems". You simply examine what you're given and what you're trying or required to do. It's self-explanatory that you're not going to bring in concepts that require multivariable calculus in a high school physics class.

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Don't assume things that are not given in a problem. You are to assume a perfect scenario. Most problems even tell you: "please ignore air resistance" or "assume no friction". In your question, a perfect scenario is that the chemical does not corrode the material of the tank, the tank has has no holes, chemical does not leak, and the chemical does not react with the elements in the atmosphere.

Excellent, excellent, excellent

Can you also advise me for what I'm about to ask?

So it is true that in mathematics you shouldnt bring other subject-fields-concepts.

Can you please, please, please describe why you shouldn't bring a leak into the problem IN THE CONTEXT OF "shouldnt bring other subject-fields-concepts."? PLEASE?

Thank you so much, you are amazing

 

[Dethrone]

This is the reason:

If no mention is made of a siphon, then you are to assume no siphoning is occurring. If no mention is made of evaporation, teleportation of material away by extraterrestrials, dipping away of material by your grandmother, etc., then you are to assume these things are not happening.

:D

I'm actually at a loss of words. Perhaps someone else could explain...:(

 

[Amad27]

This is the reason:
I'm actually at a loss of words. Perhaps someone else could explain...:(

Hi,

I asked this because of your excellent quote,

It doesn't need to be taught, it makes complete sense. For example, if you were doing an introductory calculus course on kinematics, would you assume all the factors related to air resistance and the such? No, you haven't learned it, nor does the question give you relevant data regarding the air resistance, and you're just over-thinking a basic question.

So I thought maybe a hole or a leak had something to do with an external physics or something concept.

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Once you are ready to mathematically deal with a hole in the container, then information about the hole will be given. If no mention of a hole is made, then you are to reasonably assume then that there is no hole.

If no mention is made of a siphon, then you are to assume no siphoning is occurring. If no mention is made of evaporation, teleportation of material away by extraterrestrials, dipping away of material by your grandmother, etc., then you are to assume these things are not happening.

For a well-written problem, you will be given information about everything relevant by the author of the problem that is needed to solve the problem. :D

Hi,

Thanks for this.

Question,

So the point here is that the publisher of the problem wouldn't hide something.

For

Once you are ready to mathematically deal with a hole in the container, then information about the hole will be given. If no mention of a hole is made, then you are to reasonably assume then that there is no hole.

What you are saying is that mathematically you need information, and since the hole has no information given you can't use it?

 

[MarkFL]

In the original problem, you were told the rate, as a function of time, at which there was flow into a container. You were then asked to determine the total flow into the container over a given time interval. What the fluid does once it has flowed into the container is of no relevance to answering the question.

You have to focus on what's asked, and use what's given to answer the question.

 

[Amad27]

In the original problem, you were told the rate, as a function of time, at which there was flow into a container. You were then asked to determine the total flow into the container over a given time interval. What the fluid does once it has flowed into the container is of no relevance to answering the question.

You have to focus on what's asked, and use what's given to answer the question.

A last thought on this topic,

You must make certain assumptions to answer a question (word problem)

This is the final answer, True or False?

 

[MarkFL]

I would say you frequently do have to make common sense assumptions to answer word problems in math/physics, just as you do when listening to events being recounted to you by a friend. If your friend says, "I was driving to the store the other day..." would you then wonder if he had stolen a police car and was in a high speed pursuit that happened to end at a store? These are important details that would probably not be left out. Or would you naturally assume he got into his own car, and drove reasonably within the limits of the law?

 

[Amad27]

I would say you frequently do have to make common sense assumptions to answer word problems in math/physics, just as you do when listening to events being recounted to you by a friend. If your friend says, "I was driving to the store the other day..." would you then wonder if he had stolen a police car and was in a high speed pursuit that happened to end at a store? These are important details that would probably not be left out. Or would you naturally assume he got into his own car, and drove reasonably within the limits of the law?

Very true.

That is what I really meant.

But I asked in general. Generally you would have to make certain assumptions to solve a word problem, eg. assume there is no leak/evaporation etc... but along with that you would need to use common-sense as well. =)

Is this correct? Thank you

 

[MarkFL]

I really don't know how else to say it other than if no information is given regarding a certain phenomenon, then you are to assume any aspects of this phenomenon are to be ignored.

In your original problem, a leak or evaporation would have no bearing on how much flow there was into the tank. The problem did not ask how much the container holds after the flow into it, it asked what was the total flow into the container during a given period of time. So, leaks or evaporation are irrelevant to the total amount of flow.

 

[Amad27]

I really don't know how else to say it other than if no information is given regarding a certain phenomenon, then you are to assume any aspects of this phenomenon are to be ignored.

In your original problem, a leak or evaporation would have no bearing on how much flow there was into the tank. The problem did not ask how much the container holds after the flow into it, it asked what was the total flow into the container during a given period of time. So, leaks or evaporation are irrelevant to the total amount of flow.

Hi,

I knew the leak didnt have anything to do with it. But suppose it was asking the AMOUNT in the tank after 20 minutes.
No information about the leaving rate is given.

I really don't know how else to say it other than if no information is given regarding a certain phenomenon, then you are to assume any aspects of this phenomenon are to be ignored.

This is important. You do this BECAUSE you want to solve the problem, otherwise you cant. That was all I had to say.
Which I asked you to confirm if my thought was correct there. Everyone(almost) said that it was because you could solve the problem anyway.

 

[Amad27]

This is the reason:
I'm actually at a loss of words. Perhaps someone else could explain...:(

Hey @Rido12, can you perhaps check my last comment to MarkFL as well? It would be good to hear two thoughts.

 

[I like Serena]

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