Answer
$65$ $mi/hr$
Work Step by Step
we are given that
$\frac{dx}{dt}$ = $60$ $mi/h$
$\frac{dy}{dt}$ = $25$ $mi/h$
$z^{2}$ = $x^{2}+y^{2}$
$2z\frac{dz}{dt}$ = $2x\frac{dx}{dt}+2y\frac{dy}{dt}$
$z\frac{dz}{dt}$ = $x\frac{dx}{dt}+y\frac{dy}{dt}$
$\frac{dz}{dt}$ = $\frac{1}{z}(x\frac{dx}{dt}+y\frac{dy}{dt})$
after $2$ hours
$x$ = $2(60)$ = $120$ and
$y$ = $2(25)$ = $50$
$z$ = $\sqrt {120^{2}+50^{2}}$ = $130$
so
$\frac{dz}{dt}$ = $\frac{1}{z}(x\frac{dx}{dt}+y\frac{dy}{dt})$
$\frac{dz}{dt}$ = $\frac{120(60)+50(25)}{130}$
$\frac{dz}{dt}$ = $65$ $mi/hr$
