Answer
The distance between the plane and the station is increasing at a rate of $~~296~km/h$
Work Step by Step
Let $y$ be the plane's altitude.
Let $x$ be the horizontal distance between the station and the plane.
Let $D$ be the distance between the station and the plane.
We can find $x$ one minute after the plane flies over a radar station:
$x = (300~km/h)(\frac{1}{60}~h)~cos~30^{\circ}$
$x = 4.33~km$
We can find $y$ one minute after the plane flies over a radar station:
$y = (300~km/h)(\frac{1}{60}~h)~sin~30^{\circ}+1$
$y = 3.5~km$
We can find $D$:
$D^2 = x^2+y^2$
$D = \sqrt{x^2+y^2}$
$D = \sqrt{4.33^2+3.5^2}$
$D = 5.57~km$
We can find $\frac{dD}{dt}$:
$D^2 = x^2+y^2$
$2D~\frac{dD}{dt} = 2x~\frac{dx}{dt}+2y~\frac{dy}{dt}$
$\frac{dD}{dt} = \frac{x~\frac{dx}{dt}+y~\frac{dy}{dt}}{D}$
$\frac{dD}{dt} = \frac{(4.33)(300)~cos~30^{\circ}+(3.5)(300)~sin~30^{\circ}}{5.57}$
$\frac{dD}{dt} = 296~km/h$
The distance between the plane and the station is increasing at a rate of $~~296~km/h$
