A 50 gallon tank initially contains 20 gallons of pure water. Salt solution, at 0.5 lb/gal, begins entering the tank at a rate of 4 gal/min. Simultaneously, a 2 gal/min drain is opened in the bottom of the tank. Let s(t) be the amount of salt in the tank at time t. poor (a) Set up and solve an IVP governing s(t). Don't forget an initial condition! (b) s(t) = What is the salinity of the tank (lb/gal) at the moment the tank begins to overflow?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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### Problem Description

A 50-gallon tank initially contains 20 gallons of pure water. Salt solution, at 0.5 lb/gal, begins entering the tank at a rate of 4 gal/min. Simultaneously, a 2 gal/min drain is opened in the bottom of the tank. Let \( s(t) \) be the amount of salt in the tank at time \( t \).

**(a)** Set up and solve an IVP (Initial Value Problem) governing \( s(t) \). Don't forget an initial condition!

\[ 
s(t) = \boxed{\phantom{answer}}
\]

**(b)** What is the salinity of the tank (lb/gal) at the moment the tank begins to overflow?

### Diagram and Graph Explanation

There is no graph or diagram in this problem, only a mathematical expression box to be filled out for solving the IVP.
Transcribed Image Text:### Problem Description A 50-gallon tank initially contains 20 gallons of pure water. Salt solution, at 0.5 lb/gal, begins entering the tank at a rate of 4 gal/min. Simultaneously, a 2 gal/min drain is opened in the bottom of the tank. Let \( s(t) \) be the amount of salt in the tank at time \( t \). **(a)** Set up and solve an IVP (Initial Value Problem) governing \( s(t) \). Don't forget an initial condition! \[ s(t) = \boxed{\phantom{answer}} \] **(b)** What is the salinity of the tank (lb/gal) at the moment the tank begins to overflow? ### Diagram and Graph Explanation There is no graph or diagram in this problem, only a mathematical expression box to be filled out for solving the IVP.
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