Re: [Phys-L] widget rate puzzle ... reasoning, scaling, et cetera

[Philip Keller <pkeller@holmdelschools.org>]

In terms of this question's usefulness as an educational exercise, you 
really have to know your audience.  I teach some students who can solve 
this kind of question with ease, making all of the necessary assumptions 
that you need to get the official answer. These students would enjoy 
thinking about the variations and assumption-challenging that you 
present here.

On the other hand, such questions were probably contrived (yes, 
contrived -- not real world) to provide an exercise in proportional 
thinking.  I teach some students who struggle with this and who need to 
be supported, step-by-step, week after week.  If you present these 
variations to these students, you run the risk of them throwing up their 
hands in surrender. They are already functioning at the edge, not 
completely convinced that thinking is a way to find things out.

Still, I am enjoying this thread.  Now I am picturing a machine that 
makes widgets by filling trays with goop that needs nearly 5 minutes to 
set into a widget.  The machine has room to fill up to 100 trays...



On 1/1/2015 3:56 PM, John Denker wrote:
> On 12/31/2014 06:54 PM, I wrote:
>
> > consider the following transmogrification
> > of the original question:
> >
> >       It takes 5 minutes for 5 machines to make 5 widgets.
> >       So, how many machines does it take to make 100
> >       widgets in 100 minutes?
> Here is one possible answer:  In a certain factory,
> it takes only *one* such machine to turn out 100
> widgets in 100 minutes.
>
> Spoiler:  Here's how it works, in this particular
> factory:  The machine takes four minutes and 2.5
> seconds to warm up.  Thereafter it can bang out a
> new widget every 57.5 seconds.  That means the first
> widget appears at the 5 minute mark exactly, in
> accordance with the statement of the problem.  It
> can bang out 99 more in the remaining 95 minutes,
> with a few seconds left over.
>
> This is not a contrived or unphysical possibility.
> Things like this happen in the real world all the
> time.  In addition to "warmup" issues, there are
> also "pipeline" issues.  A garden hose can put out
> a ml of water in a few milliseconds.  However, that
> does not mean that any particular ml made it all the
> way from the well to the outlet in a few milliseconds,
> or even a few seconds.  It spent a long time in the
> pipeline.  Similarly, if you buy a desktop rated at
> 10,000 bogomips, that does not mean that it can carry
> out one instruction -- from start to finish -- in 0.1
> ns or even 1 ns.  There is a lot of pipelining.
>
> =================