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Q7. A 1000 litre tank initially contains 300 litres of brine in which there is dissolved 100 grams of salt. Starting at t = 0, the mixture containing 50 grams per litre of the dissolved salt flows into the tank at the rate of 4 litres per minute. The mixture is kept uniform by stirring and well-stirred mixture simultaneously flows out of the tank at the rate of 3 litres per minute. (i) Write a differential equation that describes the rate of change of the amount of salt with time. (ii) Solve the initial value problem. (iii) How much salt will be left in the tank at the instant it overflows?

Q7. A 1000 litre tank initially contains 300 litres of brine in which there is dissolved 100 grams of salt. Starting at t = 0, the mixture containing 50 grams per litre of the dissolved salt flows into the tank at the rate of 4 litres per minute. The mixture is kept uniform by stirring and well-stirred mixture simultaneously flows out of the tank at the rate of 3 litres per minute. (i) Write a differential equation that describes the rate of change of the amount of salt with time. (ii) Solve the initial value problem. (iii) How much salt will be left in the tank at the instant it overflows?

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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Q7. = A 1000 litre tank initially contains 300 litres of brine in which there is dissolved 100 grams of salt. Starting at t = 0, the mixture containing 50 grams per litre of the dissolved salt flows into the tank at the rate of 4 litres per minute. The mixture is kept uniform by stirring and well-stirred mixture simultaneously flows out of the tank at the rate of 3 litres per minute. (i) Write a differential equation that describes the rate of change of the amount of salt with time. (ii) Solve the initial value problem. (iii) How much salt will be left in the tank at the instant it overflows?
Transcribed Image Text:Q7. = A 1000 litre tank initially contains 300 litres of brine in which there is dissolved 100 grams of salt. Starting at t = 0, the mixture containing 50 grams per litre of the dissolved salt flows into the tank at the rate of 4 litres per minute. The mixture is kept uniform by stirring and well-stirred mixture simultaneously flows out of the tank at the rate of 3 litres per minute. (i) Write a differential equation that describes the rate of change of the amount of salt with time. (ii) Solve the initial value problem. (iii) How much salt will be left in the tank at the instant it overflows?
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