Car 1 is traveling due west on Highway 60 at $40\text{ mph}$ and is $50\text{ miles}$ from the intersection of Highway 60 and Highway 95 as shown in the diagram. At the same instant, another car leaves the intersection of the two highways on Highway 95 traveling due south at $45\text{ mph}$.

At what rate is the distance between the two cars changing after $30\text{ minutes}$?