SCalceT$99\mathrm{.}3\mathrm{.}050.$EP$.$

A tank contains $1,000L$ of pure water. Brine that contains $0\mathrm{.}05$ kg of salt per liter of water enters the tank at a rate of $5\frac{L}{m}in.$ Brine that contains $0\mathrm{.}04$ kg of salt per liter of water enters the tank at a rate of $10\frac{L}{m}in.$ The solution is kept thoroughly mixed and drains from the tank at a rate of $15\frac{L}{m}in.$

Let $y(t)$ be the amount of salt $($in kg $)$ in the tank after $t$ minutes.

$($a$)$ Find the rate of change of amount of salt in the tank after $t$ minutes.

$\frac{dy}{dt}=$

$\frac{kg}{\text{m}\text{i}\text{n}}$

How much salt is in the tank when $t=0?$

$y(0)=$

How much salt $($in kg $)$ is in the tank after $t$ minutes?

$y=$

kg

$$

$($b$)$ How much salt $($in kg $)$ is in the tank after $40$ minutes? $($Round the answer to one decimal place.$)$

$y(40)=$

$kg$