Question 1105903
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With constant speeds for the two cyclists, the distance between them is changing at a constant rate.  So the 2 minutes specified in the problem is irrelevant for the calculations.<br>
Using law of cosines, if the two cyclists' speeds are 12t and 16t, then the distance d between them at time t is
{{{d(t) = sqrt((16t)^2+(12t)^2-2(16t)(12t)(cos(120))) = sqrt(256t^2+144t^2-384(-.5)(t^2)) = sqrt(592t^2) = t*sqrt(592) = (4*sqrt(37))t}}}<br>
Then {{{dd/dt = 4*sqrt(37)}}}, which shows the distance between them is changing at a constant rate.