Answer
(a) $d = 1400~km$
(b) One seismic station is not sufficient to determine the position of the epicenter.
Work Step by Step
(a) We can write an expression for the time $t_p$ for the P waves to cover the distance $d$ from the epicenter to the seismic station;
$t_p = \frac{d}{v_p}$
We can write an expression for the time $t_s$ for the S waves to cover the distance $d$ from the epicenter to the seismic station.
$t_s = \frac{d}{v_s}$
We know that:
$t_s = t_p+90~s$
Therefore, using the equation above:
$\frac{d}{v_s} = \frac{d}{v_p}+90$
$d~v_p = d~v_s+90~v_p~v_s$
$d~v_p-d~v_s = 90~v_p~v_s$
$d = \frac{90~v_p~v_s}{v_p-v_s}$
$d = \frac{(90~s)(8.5~km/s)(5.5~km/s)}{8.5~km/s-5.5~km/s}$
$d = 1400~km$
(b) One seismic station is not sufficient to determine the position of the epicenter. We can determine the distance from the seismic station to the epicenter, but we don't know in which direction. We need to combine the information from three or more seismic stations to determine the position of the epicenter.
