Two boats leave a port at the same time; one travels west at $24m\frac{i}{h}r$ and the other travels south at $32m\frac{i}{h}r.$

a$.$ After $30$ minutes, how far is each boat from port?

b$.$ At what rate is the distance between the boats changing $30$ minutes after they leave the port?

a$.$ The westbound boat is $$ from port. The southbound boat is $$

$$ from port. $($Simplify your answers.$)$

b$.$ The distance between the boats is changing at a rate of $$

$($Simplify your answer.$)$