Answer
The exhaust speed of the hot gases is 1800 m/s
Work Step by Step
We first find the rate $R$ that the mass is used.
$R = \frac{mass}{time}$
$R = \frac{250~kg}{30~s}$
$R = 8.33~kg/s$
We then find the exhaust speed $v_{ex}$ of the hot gases;
$F_{thrust} = v_{ex}~R$
$v_{ex} = \frac{F_{thrust}}{R}$
$v_{ex} = \frac{15,000~N}{8.33~kg/s}$
$v_{ex} = 1800~m/s$
The exhaust speed of the hot gases is 1800 m/s.