A train leaves a station at noon and travels east at the rate 30 mi/hr. At 2 P.M. of the same day a second train leaves the station and travels south at the rate 25 mi/hr. Express the distance d (mi) between the trains as a function of t (hr), the time the second train has been traveling.

Given answer:

$\displaystyle d = 5\sqrt{61t^2-144t+144} $

I began with:

$\displaystyle d^2 = (30t)^2+(25(t-2))^2$

Am I incorrect?