1) A tank of pure water intially contains 200 liters. Suppose that salt water solution at a concentration of 70 g/liter is piped into the tank at a rate of 3 liters/minute. The well-mixed solution is then drained out of the tank at a rate of 5 liters/minute. i) Find an expression for the volume of fluid in the tank as a function of time. ii) If y represents the total mass of salt in the tank (in grams), find a differential equation for y(t). iii) Solve (analytically) this differential equation for y, consistent with the given initial conditions. iv) When is the maximum amount of salt present in the tank? How much salt is present in the tank at this time?

1) A tank of pure water intially contains 200 liters. Suppose that salt water solution at a concentration of 70 g/liter is piped into the tank at a rate of 3 liters/minute. The well-mixed solution is then drained out of the tank at a rate of 5 liters/minute. i) Find an expression for the volume of fluid in the tank as a function of time. ii) If y represents the total mass of salt in the tank (in grams), find a differential equation for y(t). iii) Solve (analytically) this differential equation for y, consistent with the given initial conditions. iv) When is the maximum amount of salt present in the tank? How much salt is present in the tank at this time?

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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Question

1) A tank of pure water intially contains 200 liters. Suppose that salt water solution at a concentration of 70
g/liter is piped into the tank at a rate of 3 liters/minute. The well-mixed solution is then drained out of the
tank at a rate of 5 liters/minute.
i)
If y represents the total mass of salt in the tank (in grams), find a differential equation for y(t).
Find an expression for the volume of fluid in the tank as a function of time.
ii)
ii)
Solve (analytically) this differential equation for y, consistent with the given initial conditions.
iv)
When is the maximum amount of salt present in the tank? How much salt is present in the tank at
this time?

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