Answer
They will have to drill 800 meters into the granite.
Work Step by Step
We can find the time $t_w$ for the sound wave to travel through 1000 meters of water (down and back up).
$t_w = \frac{d_w}{v_w}$
$t_w = \frac{1000~m}{1500~m/s}$
$t_w = 0.67~s$
We can find the time $t_g$ the sound wave spent traveling in the granite.
$t_g = t - t_w$
$t_g = 0.94~s - 0.67~s$
$t_g = 0.27~s$
We can find the total distance the sound wave traveled through granite (down and back up).
$d_g = v_g~t_g$
$d_g = (5950~m/s)(0.27~s)$
$d_g = 1600~m$
Since the thickness of the granite is half the total distance, they will have to drill 800 meters into the granite.
