Perpendicular Motion of Ships

Let the speed of the slower ship be $s\text{ km/h}$. Then the speed of the faster ship is $s + 6\text{ km/h}$. In 2 hours, distance travelled by slower ship = $2s$. Distance travelled by faster ship = $2(s + 6)$. Since south and west directions are perpendicular, the distance between them is the hypotenuse: $(2s)^2 + (2s + 12)^2 = 60^2$. Divide by 2: $s^2 + (s + 6)^2 = 30^2 = 900$. $s^2 + s^2 + 12s + 36 = 900 \implies 2s^2 + 12s - 864 = 0 \implies s^2 + 6s - 432 = 0$. $(s + 24)(s - 18) = 0$. Since $s > 0$, $s = 18\text{ km/h}$.