Answer
$50t$
Work Step by Step
Let us consider the intersection point of $(0,0$). After $t$ hours, the coordinates of the car heading west will be $(0,-30t)$ and of the car heading north will be $(-40t,0)$.
The distance formula from $A(x_1,y_1)$ to $B(x_2,y_2)$ is
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Here, we have:
$d(t)=\sqrt{[0-(-40t)]^2+(-30t-0)^2}\\=\sqrt{1600t^2+900t^2}\\=\sqrt{2500t^2}\\=50t$
