2.21: A tank that can hold 500 gal. originally contains 200 gal. of water with 100 lbs. of salt in solution. Water containing 1 lb. of salt per gallon is entering at a rate of 3 gal/min, and the mixture is allowed to drain at a rate of 2 gal/min. Find the amount of salt in the tank at the moment when the solution begins to overflow.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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**Problem 2.21:**

A tank that can hold 500 gallons originally contains 200 gallons of water with 100 pounds of salt in solution. Water containing 1 pound of salt per gallon is entering at a rate of 3 gallons per minute, and the mixture is allowed to drain at a rate of 2 gallons per minute. Find the amount of salt in the tank at the moment when the solution begins to overflow.

**Explanation:**

This is a problem that involves understanding the rates of input and output in a tank containing a salt solution. Initially, you have a certain volume of water with a specified concentration of salt. As new water enters and drains from the tank, you need to calculate when the system reaches a critical point (overflowing) and determine the amount of salt in the tank at that time. This requires setting up and solving related differential equations regarding the rates of change for volume and salt.
Transcribed Image Text:**Problem 2.21:** A tank that can hold 500 gallons originally contains 200 gallons of water with 100 pounds of salt in solution. Water containing 1 pound of salt per gallon is entering at a rate of 3 gallons per minute, and the mixture is allowed to drain at a rate of 2 gallons per minute. Find the amount of salt in the tank at the moment when the solution begins to overflow. **Explanation:** This is a problem that involves understanding the rates of input and output in a tank containing a salt solution. Initially, you have a certain volume of water with a specified concentration of salt. As new water enters and drains from the tank, you need to calculate when the system reaches a critical point (overflowing) and determine the amount of salt in the tank at that time. This requires setting up and solving related differential equations regarding the rates of change for volume and salt.
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