Answer
$\approx$ $55.4$ $km/h$
Work Step by Step
we are given that
$\frac{dx}{dt}$ = $35$ $km/h$
$\frac{dy}{dt}$ = $25$ $km/h$
$z^{2}$ = $(x+y)^{2}+100^{2}$
$2z\frac{dz}{dt}$ = $2(x+y)(\frac{dx}{dt}+\frac{dy}{dt})$
at 4PM
$x$ = $4(35)$ = $140$
$y$ = $4(25)$ = $100$
$\frac{dz}{dt}$ = $\frac{x+y}{x}(\frac{dx}{dt}+\frac{dy}{dt})$
$\frac{dz}{dt}$ = $\frac{140+100}{260}(35+25)$ $\approx$ $55.4$ $km/h$
