Question 1185855
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        I fully agree with Edwin in that the problem has too many uncertainties in its formulation.

        The problem's formulation is at the amateur's level,  not at the professional level.



More accurate formulations would be like this:


<pre>
    Two runners are running on circular tracks each of which has a circumference of
    1320 feet. The tracks are 100 feet apart (the closest distance). The runners start 
    simultaneously from two closest points on the circles. One runner runs clockwise; 
    the other runner runs anti-clockwise.  They move at the same constant rate of 880 ft/min. 
    How fast are the runners separating when each has run 165 feet?
</pre>


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution is quite simple.


<pre>
First, notice that 165 feet is  {{{165/1320}}} = {{{1/8}}}  of the full circumference.

We can imagine that the centers of the circles  are located on x-axis of a coordinate plane.

When the runners move 165 feet each, their corresponding position vectors will be 
in position 45°  and  135° to x-axis.  So, the vectors of their speeds will be


     u = (880*cos(45°),880*sin(45°)) for one runner,  

and  

     v = (880*cos(135°),880*sin(135°))  for the other runner.


The difference of these vectors is u-v, i.e.

    (880*cos(45°)-880*cos(135°),0).


So, the separating speed is  {{{880*sqrt(2)}}},  or approximately  880*1.4142 = 1244.5 ft/minute.


At this point, the problem is just solved completely.


<U>ANSWER</U>.  The separation speed is  {{{880*sqrt(2)}}} = 1244.5 ft/minute.
</pre>

Solved.


Notice that I solved the problem without using Calculus, despite of the Edwin' suggestion.