Tricky word problems common in physics?

[Mark44]

By the way, an argument could reasonably be made that Tom and Jane were traveling by bicycle, as it would be difficult (and tedious) to drive 150 km at a constant speed of 30 km/hr.

 

[Mark44]

I have tried a meeting point which is not on the direct straight between them, but a triangle

From the problem statement: "They plan to meet at a point somewhere between them"
It's reasonable to infer that they're both moving along a straight line. If they were each traveling on one side of a triangle, the meeting point wouldn't be between them, at least by the usual meaning of "between."

 

[Antisthenes]

One of the main reasons I like math is that there are no excuses. You can't hide.

The math book is called Sinus 1T. It's probably the most popular high school math book in Norway, used by those who want to study physics or math at the university. The book is used by many high schools. Therefore I find it hard to believe that it contains this kind of error.

Have checked it several times now that it says "112.5 km", and that the assignment number 3.178, in the solution chapter, page 484, is related to the assignment number 3.178 on page 365. (I got narcolepsy, so often triple check things in order to avoid mistakes.)

On the other hand, it might be relevant indeed to mention that the original text is actually ambiguous in Norwegian, since it says that it takes Tom three hours to drive "the whole stretch", which in Norwegian often refers to the particular distance a person intends to travel, but it can also refer to the whole stretch of 150 km.

Upon reflection I assume that the book doesn't contain an error, and that I jumped to conclusions when reading the sentence "the whole stretch", right?

 

[martinh]

One of the main reasons I like math is that there are no excuses. You can't hide.

The math book is called Sinus 1T. It's probably the most popular high school math book in Norway, used by those who want to study physics or math at the university. The book is used by many high schools. Therefore I find it hard to believe that it contains this kind of error.

Have checked it several times now that it says "112.5 km", and that the assignment number 3.178, in the solution chapter, page 484, is related to the assignment number 3.178 on page 365. (I got narcolepsy, so often triple check things in order to avoid mistakes.)

On the other hand, it might be relevant indeed to mention that the original text is actually ambiguous in Norwegian, since it says that it takes Tom three hours to drive "the whole stretch", which in Norwegian often refers to the particular distance a person intends to travel, but it can also refer to the whole stretch of 150 km.

Upon reflection I assume that the book doesn't contain an error, and that I jumped to conclusions when reading the sentence "the whole stretch", right?

Tom is traveling at 50 km/h and Jane at 30 km/h. Tom starts an hour earlier, so travels for (1+t) hours compared to t hours for Jane.

So,

50 (1+t) + 30 t = 150

Thus, t = 1.25 hours

Distance traveled by Tom is 50 (1+t) = 112.5 km.

The book is correct.

 

[tnich]

Tom is traveling at 50 km/h and Jane at 30 km/h. Tom starts an hour earlier, so travels for (1+t) hours compared to t hours for Jane.

So,

50 (1+t) + 30 t = 150

Thus, t = 1.25 hours

Distance traveled by Tom is 50 (1+t) = 112.5 km.

The book is correct.

However, that would make Tom's travel time 2.25 hrs. The problem states that his travel time is 3 hrs. How did you decide that his speed is 50km/hr?

 

[tnich]

However, that would make Tom's travel time 2.25 hrs. The problem states that his travel time is 3 hrs. How did you decide that his speed is 50km/hr?

Oh, I see. I missed post #43.

 

[martinh]

However, that would make Tom's travel time 2.25 hrs. The problem states that his travel time is 3 hrs. How did you decide that his speed is 50km/hr?

The original statement of the problem in English was a mis-translation of the Norwegian. Tom would take 3 hours to travel the whole distance (150km) and Jane would take 5 hours to travel the whole distance (150 km).

 

[gleem]

Yes, otherwise Tom would have had to know Jane's speed in order to have arrived at the meeting point in three hours.

 

[gmax137]

well, if nothing else this all points out one of the most important things about "doing" word problems: when translating the words into mathematics, it is essential that the translation is what the words say, not what you think they say. Many erroneous answers come from misinterpreting the text.

The only clue that this was going on in this thread was how easy the answer was: if jane drives 3-1 = 2 hours at 30 km/hour she went 60 km so tom must have gone 150-60 = 90. There is no "substitution" there, I'm thinking this is too easy. You don't even need Toms speed to get it.

 

[Antisthenes]

It wasn't really a wrong translation either. Because in Norwegian it actually seems like "the whole stretch" refers to the meeting point, and not the distance of 150 km. However, I have almost no experience with word problems, so didn't know that they are allowed to be that tricky and ambiguous. But if I also had more experience with solving problems related to distance, rate and time, I would have quickly found and applied the same equation as martinh, and seen the correct answer. Instead I got lost in all the equations I studied when reading different books about how to solve word problems. No excuse, however, because if I had been good at math, I would have found the solution much sooner in any case.

 

[gmax137]

I didn't know that they are allowed to be that tricky and ambiguous.

They shouldn't be tricky that way.

 

[Antisthenes]

Well, to be fair, I assume the authors took it for granted that the reader had enough knowledge to quickly try both alternatives and discover the right solution. A noob like me, however... :)

 

[Mark44]

I have almost no experience with word problems, so didn't know that they are allowed to be that tricky and ambiguous.

They shouldn't be tricky that way.

I agree. The wording of this type of problem should be unambiguous.

Well, to be fair, I assume the authors took it for granted that the reader had enough knowledge to quickly try both alternatives and discover the right solution. A noob like me, however... :)

No, I don't think so. Possibly they didn't realize that their wording was ambiguous. As a general rule, textbook authors are more careful than this -- they don't expect a student to have to work a problem two different ways to get two different answers.

 

[Antisthenes]

The authors should have clearly seen this ambiguity. In common Norwegian it's natural to read "the whole stretch" as referring to the preceding sentence which mentions the meeting place where they wish to meet, and not referring to the first sentence which mentions that they live 150 km apart.

There are three reasons why I interpreted "the whole stretch" as "the whole journey" and translated it simply as "the journey": 1) In Norwegian, "stretch" and "journey" often mean the same thing. 2) In Norwegian, it would be better to have written "strekket", which is more general, and not "strekningen" if the sentence referred to the distance of 150 km. 3) If somebody wishes to travel somewhere and thinks that he or she will need 3 hours to drive "the whole stretch", then it's reasonable to assume that "the whole stretch" refers to the whole journey that he or she wishes to travel.

However, two sentences later one notices that "the whole stretch" may not refer to the journey after all. Have translated the entire text here, word for word, though the characters have Norwegian names in the original, while I call them Tom and Jane:

"Tom and Jane live 150 km apart. They wish to meet at a place in an area between them. Tom thinks he can drive the whole stretch on 3 hours with his scooter. He drives from home at 12:00. Jane doesn't entirely trust her moped, so she believes that she needs 5 hours on 150 km. She drives from home at 13:00. How far away is the meeting place from where Tom lives?"

If I had been more familiar with word problems, and the carefulness they demand, I would have known that people in this forum needed a word for word-translation. But this is basically the first word problem I have struggled with, making it more difficult since I also lack experience with problems involving rate, time and distance, so mistakes happened during the information overload.

The lesson learned, once again, is that math is not a field where you can fight above your weight class, and that if you try to learn math on your own, with no teacher, you can easily end up with knowledge gaps that you are not even aware of: swimming happily around in the ocean without noticing the undercurrents.

So be very grateful if you are in a good class, at school, with a good teacher. Because math and physics are the areas of science where one can be really creative, today and in the future, and then you don't want to end up like a math illiterate student in the humanities. Nietzsche, by the way, regretted that he didn't know math and physics. Though philosophy is still a good path if one seeks wisdom more than science.

 

[fresh_42]

The authors should have clearly seen this ambiguity.

I'm not so sure, but this can't be said without knowing the original text. A sloppy translation is more likely.

 

[Antisthenes]

Word for word, the translation is very accurate, though some sentences don't sound entirely right in English, as far as I can tell, when translating it word for word. The only word that could have been translated with more precision is "thinks", which in the original has a meaning which lies between thinking, assuming and calculating, but that particular word is not relevant here anyway.

Even in English it should be pretty obvious that the assignment is ambiguous, because "the whole stretch" can refer to both the whole journey and the whole distance of 150 km. Unless there is some special "math speak" here I'm not aware of.

 

[Mark44]

Word for word, the translation is very accurate, though some sentences don't sound entirely right in English, as far as I can tell, when translating it word for word.

A word for word translation is less important than capturing the meaning.

The only word that could have been translated with more precision is "thinks", which in the original has a meaning which lies between thinking, assuming and calculating, but that particular word is not relevant here anyway.

I agree. It makes no difference in the underlying meaning of the problem.

Even in English it should be pretty obvious that the assignment is ambiguous, because "the whole stretch" can refer to both the whole journey and the whole distance of 150 km. Unless there is some special "math speak" here I'm not aware of.

No, there's no "math speak" here. "Whole stretch" is ambiguous if it could be interpreted to mean either the distance one of the people covered or the whole 150 km.

 

[Antisthenes]

Here is the original text in Norwegian, on page 365 in Sinus 1T, (2014). Anyone who speaks Norwegian will confirm that it's very reasonable to interpret "the whole stretch" as referring to the whole journey:

"Vibeke og Viktor bor 150 km fra hverandre. De ønsker å møtes et sted i området mellom der de bor. Vibeke regner med at hun kan kjøre hele strekningen på 3 timer med skuteren sin. Hun kjører hjemmefra kl. 12.00. Viktor stoler ikke helt på mopeden sin, så han tror han trenger 5 timer på 150 km. Han kjører hjemmefra kl. 13.00. Hvor langt ligger møtestedet fra der Vibeke bor?"

If anyone still doubts it, I can upload an image of page 365. Notice however that I switched gender in my first quick translation of the text, since math is gender blind anyway and I didn't think this was going to turn into an academic debate about hermeneutics.

 

[fresh_42]

And here's what Google translate made out of it:

"Vibeke and Viktor live 150 km apart. They want to meet somewhere in the area between where they live. Vibeke expects her to run the whole stretch of 3 hours with her skipper. She runs from home at. 12:00. Viktor does not trust his mop, so he thinks he needs 5 hours at 150 km. He runs from home at. 13:00. How far is the meeting place from where Vibeke lives?"

I read this as 50 km/h for Vibeke rather than a total traveling time of three hours, because the reference to the meeting point is mentioned not before the last question, i.e. the rest before describes the setup.

They plan to meet at a point somewhere between them. Tom uses 3 hours on the journey.

changes the description significantly.

 

[Antisthenes]

All Norwegians will concur that in this context it's perfectly reasonable to conclude that "the whole stretch" refers to the intended journey, not the distance of 150 km.

Partly because in Norway it's common to use the word "strekning" when discussing a journey or travel distance. Secondly, if you are meeting a friend at a place between where you and him live, and he says that he assumes/expects/guesses that it will take him 3 hours to drive the whole stretch on his scooter, then you will conclude that he intends to meet you at that place in three hours. That is how I naturally read the text the first time.

However, I was a bit puzzled when starting to reflect upon why the text also mentioned that it took 5 hours to travel 150 km, but discovered that many word problems are often worded in a rather unusual or complicated way, so I chose the interpretation that came to mind the first time I read the text.

I wanted to find a way to solve this problem, so from this point of view it would be totally irrational and not in my own self-interest to knowingly present a misleading translation in this forum. But it would have been better if I had written a word for word translation, because other people would then have suggested alternative interpretations of this ambiguous text.

In any case, precision is important in math, and the authors should therefore simply have written: "Vibeke calculates that it will take her 3 hours to travel 150 km", instead of using a vague word like "the whole stretch".

By the way, Philip Tetlock and Robert Jervis present interesting research on why people, in the intelligence community for example, end up with different interpretations of texts and situations, even when they sincerely think that their own interpretation is the right one.

So you may disagree with my interpretation of the assignment, but nobody can claim that the text is not ambiguous, especially if they are familiar with Norwegian.

 

[Antisthenes]

In science, one must provide evidence when making statements, so for the sake of conscientiousness I will give some examples of how the word "stretch" is used in Norwegian. Anyone who still cares about this topic can then use Google translator to check that it's very reasonable in Norwegian to assume that "the whole stretch" refers to Vibeke's journey, and not the distance of 150 km.

For example, in Norwegian one can talk about "my stretch", "your stretch" or "our stretch" when planning a journey or discussing a distance where you are doing some activity. The national railway company in Norway created an app where one can click on "My stretch" ("Min strekning") to check if your train is delayed, as described at the end of this article here:

https://www.dinside.no/reise/na-blir-det-lettere-a-sjekke-togtidene/61632988

Here you will also notice that in Norwegian it's perfectly acceptable to talk about a "train stretch" ("togstrekning"), or a "boat stretch" or "bus stretch" for example, as seen in the headline of this newspaper article:

http://www.avisa-hordaland.no/vaksdal/togstrekninga-mellom-dale-og-stanghelle-er-no-open-1.1909555

If you ask a Norwegian about how his journey was, he might reply: "It was awful, it was snow on the whole stretch", as opposed to snowing on only a part of it.

In Norwegian, the word "stretch" is not necessarily an abstract mathematical concept. It's often used in a much more concrete way.

Consequently, when my math book mentioned that Vibeke was planing a journey and that she thought it would take 3 hours to travel "the whole stretch", on her scooter, it was natural to conclude that it referred to her journey: her stretch, on a scooter - or her "scooter stretch", so to speak. The authors should have been aware of that.

The assignment is ambiguous, even in English, because if a person is driving straight to a specific location, why would she calculate how long it takes to travel to a different location? In our context, that doesn't make sense.

Unfortunately, math books in Norway don't have the highest standard. For example, many high schools use the book "Sigma 1T" instead of "Sinus 1T". I decided to use the latter book, after reading how "Sigma 1T" presents the PEMDAS rule, on page 14:

"1. First we calculate exponents if there are any.

2. Then we do multiplications and divisions.

3. Finally, we put it together, through calculation, and find the answer".

https://issuu.com/gyldendalnorskforlag/docs/sigma1t_bla-i-bok

"Calculating together" is probably the most accurate word for word-translation of the Norwegian expression "regne sammen", which means to put something together through counting or calculation. The authors don't care to mention addition and subtraction. They just assume that the reader will somehow figure out that "calculating together" refers to addition and subtraction. And one must read the rest of the page to notice that "If an expression stands within a parenthesis, we begin by "calculating out" ("regne ut") that expression".

Why is the education system pretty rotten in the state of Norway? Well, we have a rather left-wing culture and the government thinks that many children will suffer if they are forced to do math at school. The result is that many teachers don't know what they are doing, which ironically creates frustration and stress in the class room, so children suffer anyway, especially later in life.