## Related questions with answers

Question

In this exercise, a 1000-liter tank contains 500 L of water with a salt concentration of 10 g/L. Water with a salt concentration of 50 g/L flows into the tank at a rate of $R_{\text {in }}$=80 L/min. The fluid mixes instantaneously and is pumped out at a specified rate $R_{\text {out. }}$ Let y(t) denote the quantity of salt in the tank at time t.

Assume that $R_{\text {out }}$=40 L/min.

(a) Set up and solve the differential equation for $y(t)$.

(b) What is the salt concentration when the tank overflows?

Solution

VerifiedStep 1

1 of 13$\dfrac{dy}{dt}$ is the difference between the two rates of change:

$\dfrac{dy}{dt}=Rate_{in}-Rate_{out}$

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