Answer
$8.99$ $ft/s$
Work Step by Step
we are given that
$\frac{dx}{dt}$ = $4$ $ft/s$
$\frac{dy}{dt}$ = $5$ $ft/s$
$z^{2}$ = $(x+y)^{2}+500^{2}$
$2z\frac{dz}{dt}$ = $2(x+y)(\frac{dx}{dt}+\frac{dy}{dt})$
15 minutes after the woman starts we have
$x$ = $(4 ft/s)(20min)(60s/min)$ = $4800$ $ft$
$y$ = $5(15)(60)$ = $4500$
$Z$ = $\sqrt {(4800+4500)^{2}+500^{2}}$ = $9313.43$
$\frac{dz}{dt}$ = $\frac{x+y}{z}(\frac{dx}{dt}+\frac{dy}{dt})$
$\frac{dz}{dt}$ = $\frac{4800+4500}{9313.43}(4+5)$ = $8.99$ $ft/s$
