04-05 Water flowing into triangular trough

Volume of water:
$V = \frac{1}{2}xy (10) = 5xy$
 

By similar triangle:
$\dfrac{x}{y} = \dfrac{4}{4}$

$x = y$
 

$V = 5y^2$

$\dfrac{dV}{dt} = 10y \dfrac{dy}{dt}$
 

when y = 6 in or 0.5 ft
$3 = 10(0.5) \dfrac{dy}{dt}$

$\dfrac{dy}{dt} = 0.6 \, \text{ ft/min}$           answer

Volume of water:
$V = \frac{1}{2}xy (10) = 5xy$
 

By similar triangle:
$\dfrac{x}{y} = \dfrac{6}{3}$

$x = 2y$
 

$V = 5(2y)y = 10y^2$

$\dfrac{dV}{dt} = 20y \dfrac{dy}{dt}$
 

when y = 6 in or 0.5 ft
$12 = 20(0.5)\dfrac{dy}{dt}$

$\dfrac{dy}{dt} = 1.2 \, \text{ ft/min}$           answer