Answer
The distance between the cars is increasing at a rate of $65~mi/h$
Work Step by Step
Let $z$ be the distance between the two cars. We can find $z$ after 2 hours:
$z^2 = x^2+y^2$
$z = \sqrt{x^2+y^2}$
$z = \sqrt{(50~mi)^2+(120~mi)^2}$
$z = 130~mi$
We can differentiate both sides of the equation with respect to $t$:
$z^2 = x^2+y^2$
$2z~\frac{dz}{dt} = 2x~\frac{dx}{dt} + 2y~\frac{dy}{dt}$
$\frac{dz}{dt} = \frac{1}{z}~(x~\frac{dx}{dt} + y~\frac{dy}{dt})$
$\frac{dz}{dt} = \frac{1}{130}~[(50)(25) + (120)(60)]$
$\frac{dz}{dt} = 65~mi/h$
The distance between the cars is increasing at a rate of $65~mi/h$.