Question 1178358
Kim and Ken traveled at the same time at the rate of 20 m/min, from the same point on a circular track of radius 600 m. If Kim walks along a circumference and {{{cross(Kim)}}} Ken towards the center, find their distance after 10 minutes.
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<pre>
After 10min at 20m/min, they have eached walked 10min*20m/min = 200m.

Let A denote Kim's final position
Let B denote Ken's final position
and C be the center of the circular track

Draw triangle ABC.  

The distance between Kim and Ken is |AB|
|AC| is just a radius, 600m
|BC| is just the radius minus the distance Ken traveled in towards the center:
    600m-200m = 400m 

We know Kim swept out an angle equal to x, where we can set up a proportion of her distance along the circumference with the total circumference:
 {{{ x/200 = (2*pi)/(2*pi*600) }}}  or  
   {{{ x = (1/3) }}} radians

Using the Law of Cosines:

{{{ abs(AB) = sqrt(abs(AC)^2+abs(BC)^2-2*abs(AC)*abs(BC)*cos(x)) }}}

Plug in all the values to get:
{{{ abs(AB) }}} &#8776; {{{ 257.72m}}}