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bigfoot66
bigfoot66
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June 13th, 2012 at 10:27:10 AM permalink
Quote: Doc

When I was an undergraduate, I came home one weekend, and my mother told me that there had been a big flap. My younger brother in elementary school had missed a question on a math test and didn't understand why his answer was wrong. He gave the problem to our father who shared it with the group of engineers he worked with. They agreed with my brother's answer, but the teacher still disagreed. I read the problem and immediately recognized why there was disagreement.

Of course, I don't remember the exact problem, but it went something like this:

You may answer (a) and (b), but my additional question is this: Why was there such disagreement on the answer to part (b)? (No, it was not just someone's incompetence at arithmetic.)



B makes it clear that our traveler is going 10 miles further on the express train but does not explain if that is at the expense of 20 miles on the local segment. I would imagine the teacher was looking for 60/20 and then 70/10, but it does not make much sense to interpret the question that way as the train station could not move 10 miles. We should assume that he went from 60/20 to 70/20.
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Doc
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June 13th, 2012 at 10:34:19 AM permalink
So what's the "other" answer to (b)?
Wizard
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Wizard
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June 13th, 2012 at 10:37:53 AM permalink
RE: bigfoot's "other interpretation."

I hope nobody will mind that I say that bigfoot's interpreation is that the passenger got on the express train at a stop 10 miles further away from his destination, and changed trains at the usual station. That is certainly not how I interpreted the problem. However, I think if the question is ambiguous then any fault should lie (or is it lay) with the person framing the question. That said, if I were the teacher I would accept bigfoot's solution as well.

Quote: Doc

So what's the "other" answer to (b)?



49.090909... MPH.
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Doc
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June 13th, 2012 at 10:47:21 AM permalink
That is exactly what was the disagreement. After almost half a century, I'm not completely sure, but I think the teacher used the Wizard's original interpretation, while my brother and the engineers used bigfoot66's interpretation. The teacher was not as accepting of other viewpoints as the Wizard seems to be. I think it was a case of believing, "The answer book is never wrong."

As a grad student/TA and later as the instructor, my experience was often that, "The answer book is rarely right." I formed the opinion that college solution manuals were often prepared by the professor/author's student assistant who had to prepare hundreds/thousands of solutions in as little time as possible at the lowest rate paid on campus. Result: lots of errors.
Wizard
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Wizard
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June 13th, 2012 at 11:05:03 AM permalink
Quote: Doc

As a grad student/TA and later as the instructor, my experience was often that, "The answer book is rarely right." I formed the opinion that college solution manuals were often prepared by the professor/author's student assistant who had to prepare hundreds/thousands of solutions in as little time as possible at the lowest rate paid on campus. Result: lots of errors.



I wish I could get back all the time I spent beating my head against the wall because of incorrect answers in the "back of the book." In my old high school math books the error rate was quite high. You would think the publisher could pay at least two people to work through all the problems to make sure two heads come up with the same answer.

Back the problem, I think anyone familiar with taking commuter trains would interpret it my way, especially in New York, where trains on the same route run at different speeds. It is also normal for people to go from point A to B over and over, but the time of the commute might change depending on the availability of express trains.
It's not whether you win or lose; it's whether or not you had a good bet.
s2dbaker
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June 13th, 2012 at 11:28:36 AM permalink
The original post is deceptively complicated. Basically, it all boils down to: a hat floats in a river for 20 minutes and travels one mile. How many miles will it travel in an hour?
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Doc
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June 13th, 2012 at 11:40:52 AM permalink
Quote: s2dbaker

The original post is deceptively complicated. Basically, it all boils down to: a hat floats in a river for 20 minutes and travels one mile. How many miles will it travel in an hour?


Except it takes a little figuring to know that it took 20 minutes for it to float that mile.
FleaStiff
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June 13th, 2012 at 1:33:20 PM permalink
Quote: Doc

As a grad student/TA and later as the instructor, my experience was often that, "The answer book is rarely right." I formed the opinion that college solution manuals were often prepared by the professor/author's student assistant who had to prepare hundreds/thousands of solutions in as little time as possible at the lowest rate paid on campus. Result: lots of errors.



I believe that Steve Wolfram, the creator of Mathematica, faced the same problem when checking his computer program against authoritative sources. His program would often give different answers .... and it turns out it was the sample inputs he had taken from recognized authorities were in the wrong.

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