Answer
$13$ $ft/s$
Work Step by Step
Given $\frac{dh}{dt}$ = $5$ and $\frac{dx}{dt}$ = $15$
find $\frac{dz}{dt}$
$z^{2}$ = $x^{2}+h^{2}$
$2z\frac{dz}{dx}$ = $2x\frac{dx}{dx}+2h\frac{dh}{dx}$
$\frac{dz}{dt}$ = $\frac{1}{z}(15x+5h)$
when $t$ = $3$
$h$ = $45+3(5)$ = $60$ and
$x$ = $15(3)$ = $45$
$z$ = $\sqrt {45^{2}+60^{2}}$ = $75$
so
$\frac{dz}{dt}$ = $\frac{1}{z}[15(45)+5(60)]$ = $13$ $ft/s$
