Answer
The runner will reach home plate 0.27 seconds before the ball reaches home plate.
Work Step by Step
We can find the speed at which the ball was thrown:
$x = \frac{v_0^2~sin(2\theta)}{g}$
$v_0 = \sqrt{\frac{gx}{sin(2\theta)}}$
$v_0 = \sqrt{\frac{(9.80~m/s^2)(65~m)}{sin(2\times 30^{\circ})}}$
$v_0 = 27.1~m/s$
We can find the time it takes the ball to reach home plate;
$t = \frac{x}{v_x} = \frac{65~m}{(27.1~m/s)~cos(30^{\circ})}$
$t = 2.77~s$
We can find the time it takes the runner to reach home plate;
$t = \frac{d}{v} = \frac{20~m}{8.0~m/s}$
$t = 2.5~s$
The runner will reach home plate 0.27 seconds before the ball reaches home plate.
