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Subject:   RE: teacher needs help!
Author: Mathman
Date: Dec 16 2004
On Dec 14 2004, magnus wrote:
> Hi, I teach calculus at a rural school, and am having problems with
> a particular word problem.  

It reads as follows:  A car
> traveling north at 60 mph and a truck traveling east at 45 mph leave
> an intersection at the same time. At what rate is the distance
> between them changing 2 hours later?

The answer in the answer key
> is 75 mph which would be the pythogorean triple of 45 and 60.
> However, when I work the problem out with what I know about related
> rates (and it seems that you all know a lot more than me) I get
> approximately 74.2 mph.  

Who is right?  Is the real answer 75,
> and it is just a coicidence that 75 is the pythogorean triple?  What
> answer do you get, and how did you get it?  To solve this problem,
> I'm using the concept of "related rates, dx/dt, & dy/dt," which
> would make sense, since that is the title of the section this
> problem comes from.

Thanks for helping.
John Jones
Trenton R-9
> Missouri

You have been given some good advice already.  I'd suggest that you go over a
fair number of such problems if you are to teach this topic well to your
students.  It is fundamental to their studies in the subject.  Also consider
looking at some with rather more difficulty to expand their knowledges and
skills before university.  In our present courses there is one such introductory
problem that actually starts the exercise and it has a train going over a
bridge, height given, while a boat travels underneath at 90 degrees to the
direction of the train.  That is; it is in three dimensions.  It might be
worhtwhile considering the same problem you outline with those restrictions as
well.  Some have also done problems of rather more difficulty, so it's worth
going over the material to that extent for them.  A quite good source of
exercises of typical problems and solutions might be found in the Schaums
Outline Series.


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