By cosine law:

$s^2 = [ \, 60(t - 7/60) \, ]^2 + (42 - 30t)^2 - 2[ \, 60(t - 7/60) \, ](42 - 30t) \cos 60^\circ$

$s^2 = (3600t^2 - 840t + 49) + (1764 - 2520t + 900t^2) - (-1800t^2 + 2730t - 294)$

$s^2 = 6300t^2 - 6090t + 2107$

$s = \sqrt{6300t^2 - 6090t + 2107}$

$\dfrac{ds}{dt} = \dfrac{12600t - 6090}{2\sqrt{6300t^2 - 6090t + 2107}} = 0$

$12600t - 6090 = 0$

$t = 29/60 \, \text{ hr}$

$t = 29 \, \text{ min}$

Time: 12:29 PM *answer*