Question 1065804
.
When I read this problem condition yesterday morning, automatic switcher worked in my mind/(undermind), and another/different 
version came to my conscionsness:


<pre>
    A rower goes upstream on a river. &nbsp;When passing under a bridge, &nbsp;a bottle of whiskey falls into the water.
    Since it's half-full, &nbsp;it floats. &nbsp;The rower doesn't notice it, &nbsp;and continues going upstream.
    After &nbsp;20 minutes, &nbsp;he gets thirsty and looks for the bottle. &nbsp;Having sobered some, &nbsp;he figures out that it fell into the water.
    He turns around and rows downstream. &nbsp;He finds the bottle &nbsp;1 mile from the bridge. &nbsp;Find the speed of the current.
</pre>

Yesterday in the evening I got understanding that I actually solved DIFFERENT problem than the original.


But thinking about the subject, I then got understanding that this SECOND formulation is actually BETTER than the original, 
and is much more NATURAL.


Why ?? - If you read attentively both formulations, you will get "why".


The second formulation, which came from "my undermind" is much more natural from the point of view of human motivation than the original.


Indeed, <U>WHO</U> with the healthy mind will start rowing against the current to get the bottle ??
Much simpler is to stay "in place" and to wait when the current will bring/deliver the bottle.


So, now I think (and I am 120% sure) that my undermined formulation is much better, is much more realistic and is much more similar/closer  
to the classic, than that what came first.


So, my solution below and everything what follows relates to the <U>UPDATED formulation</U>, and <U>NOT TO THE ORIGINAL ONE</U>.


Sorry that this new understanding came with a delay. But later is better than no-when.


<BLOCKQUOTE><TABLE BORDER=2>
  <TR>
  <TD>
&nbsp;&nbsp;&nbsp;&nbsp;I checked my sources, and now my statement is:&nbsp;&nbsp;&nbsp;&nbsp;


&nbsp;&nbsp;&nbsp;&nbsp;My changed formulation IS CLASSICAL.


&nbsp;&nbsp;&nbsp;&nbsp;That which came originally, IS NOT.


  </TD>
  </TR>
</TABLE></BLOCKQUOTE>

/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\


This problem is classic Travel and Distance problem.  (with the corrections above !!)
Edwin provided its classic solution.


But his solution requires a powerful imagination.
For those who experiences a lack of such imagination (as myself), I will give another solution.


<pre>
Let "u" be the rower speed in "still water" and "v" be the current speed (in miles per hour). 


From that moment, when the rower figured out that the bottle fell into water,
from the same moment when he turned around and start catching the bottle, we have a classic "catching up" problem.


Namely, we have the rower at the distance of {{{(u-v)*(1/3)}}} upstream the bridge, and we have a bottle at the distance {{{v*(1/3)}}} downstream the bridge.

What is {{{1/3}}} here ? - But of course, it is {{{1/3}}} of an hour, or 20 minutes.


At this moment we turn ON our chronometer, we start counting the time, and what we see ? What do we observe ?

Starting from this moment and till the moment "t" of catching up the bottle, the rower will cover the distance 

D = (the distance back to the bridge) + (the distance the bottle went downstream in {{{1/3}}} of an hour) + (the distance bottle went downstream during the time "t") = 

         {{{(u-v)*(1/3)}}}                     +     {{{v*(1/3)}}}                                                       +     {{{v*t}}} = 

       = {{{u*(1/3) - v*(1/3) + v*(1/3)}}} + {{{v*t}}} = {{{u*(1/3)}}} + {{{v*t}}}.


Calculating this distance by another way (using the speed (u+v) of the rower downstream) we can express this distance as

D = {{{(u+v)*t}}}.


The distance is the same (!!!), so we have an equation 

{{{u*(1/3)}}} + {{{v*t}}} = {{{(u+v)*t}}}.

Simplify it in one more step, and you get A <U>REMARKABLE EQUALITY</U>:

         t = {{{1/3}}}.

Which means (and we <U>PROVED</U> it) that the catching time is exactly {{{1/3}}} of an hour.

The thing which was not obvious from the beginning !


Now we are at the finish line. One step to the end. To the VICTORY !!


We have another condition: for 20 minutes plus "t" minutes the bottle traveled exactly one mile !

It means that {{{(1/3)*v + (1/3)*v}}} = 1,  or  {{{(2/3)*v}}} = 1,  or  (AT LAST !!!)  v = {{{3/2}}} miles per hour.
</pre>

&nbsp;&nbsp;&nbsp;&nbsp;SOLVED.  &nbsp;&nbsp;&nbsp;&nbsp;SOLVED. &nbsp;&nbsp;&nbsp;&nbsp;SOLVED.   



---------------------
I am a mathematician by my basic education, so my mind works automatically in attempting to reverse / to transform the nonsense to 
some sensible. So it was in this case (as in many other cases).



''''''''''''''''''''''''''''
Now I have a question to the person who posted (or invented ?) the original post:



Why (or for what reason) do you distribute this original the half-false formulation of the beautiful problem 
carefully designed hundreds years ago by those who really know and love MATH ???


The problems like this one (corrected by me) are/is a treasure, literally.


And they require an adequate treatment, too.