17-18 Rate of shadow in the wall of a building

$y = \dfrac{180}{x}$

$\dfrac{dy}{dt} = \dfrac{-180\dfrac{dx}{dt}}{x^2}$
 

when x = 30 - 15 = 15 ft
$\dfrac{dy}{dt} = \dfrac{-180(5)}{15^2}$

$\dfrac{dy}{dt} = -4 \, \text{ ft/sec}$           answer
 

The negative sign in the answer indicates that the length of the shadow is shortening.

$y = 10 - \dfrac{120}{x}$

$\dfrac{dy}{dt} = - \dfrac{-120\dfrac{dx}{dt}}{x^2}$

$\dfrac{dy}{dt} = \dfrac{120}{x^2}\,\dfrac{dx}{dt}$
 

when x = 30 - 15 = 15 ft
$\dfrac{dy}{dt} = \dfrac{120}{15^2}\,(5)$

$\dfrac{dy}{dt} = \dfrac{8}{3} \, \text{ ft/sec}$           answer