All three runners finish together. <p/>


Let the radius of <i>R</i>`s track be <i>r</i> and let the radius of the 
first semicircle of <i>P</i>`s track be <i>p</i>; then the radius of the 
second semicircle of this track is <i>r</i> <font face="symbol">-</font
> <i>p</i>. The total length of 
<i>P</i>`s track is <font face="symbol">p</font
><i>p</i> + <font face="symbol">p</font
>(<i>r</i> <font face="symbol">-</font
> <i>p</i>) = <font face="symbol">p</font
><i>r</i>, the same as the 
length of <i>R</i>`s track. <p/>


By a simlar argument, the length of <i>Q</i>`s 
track is also <font face="symbol">p</font
><i>r</i>, so all three runners finish at the same time.   




    


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