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A tank with a capacity of 250 gallons initially contains 100 gallons of a solution containing 5 pounds of salt. Fresh water enters at a rate of 3 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. Find an expression for the the amount of salt Q(t) (in pounds) in the tank t minutes after the process begins, up to the moment when the tank is full. Use it to compute the amount of salt in the tank at the moment when the tank is filled up.

A tank with a capacity of 250 gallons initially contains 100 gallons of a solution containing 5 pounds of salt. Fresh water enters at a rate of 3 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. Find an expression for the the amount of salt Q(t) (in pounds) in the tank t minutes after the process begins, up to the moment when the tank is full. Use it to compute the amount of salt in the tank at the moment when the tank is filled up.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A tank with a capacity of 250 gallons initially contains 100 gallons of a solution containing 5 pounds of salt. Fresh water enters at a rate of 3 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. Find an expression for the the amount of salt Q(t) (in pounds) in the tank t minutes after the process begins, up to the moment when the tank is full. Use it to compute the amount of salt in the tank at the moment when the tank is filled up.
Transcribed Image Text:A tank with a capacity of 250 gallons initially contains 100 gallons of a solution containing 5 pounds of salt. Fresh water enters at a rate of 3 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. Find an expression for the the amount of salt Q(t) (in pounds) in the tank t minutes after the process begins, up to the moment when the tank is full. Use it to compute the amount of salt in the tank at the moment when the tank is filled up.
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