6. A tank contains 200 liters of pure water. Brine containing 1kg of salt per liter runs into the tank at the rate of 3 liters per minute. The solution is mixed and runs out of the tank at the same rate. (a) Find an initial value problem to model this scenario. Be sure to use correct units and show your work. Do not solve the equation. (b) What if the water runs out of the tank at only 2 liters per minute instead of 3? This means that each minute the volume of liquid in the tank will increase by 1 liter. How does that affect the initial value problem from part (a)? (Assume the tank is large enough so it doesn't overflow.)

6. A tank contains 200 liters of pure water. Brine containing 1kg of salt per liter runs into the tank at the rate of 3 liters per minute. The solution is mixed and runs out of the tank at the same rate. (a) Find an initial value problem to model this scenario. Be sure to use correct units and show your work. Do not solve the equation. (b) What if the water runs out of the tank at only 2 liters per minute instead of 3? This means that each minute the volume of liquid in the tank will increase by 1 liter. How does that affect the initial value problem from part (a)? (Assume the tank is large enough so it doesn't overflow.)

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

6. A tank contains 200 liters of pure water. Brine containing 1kg of salt per liter runs into the
tank at the rate of 3 liters per minute. The solution is mixed and runs out of the tank at the
same rate.
(a) Find an initial value problem to model this scenario. Be sure to use correct units and
show your work. Do not solve the equation.
(b) What if the water runs out of the tank at only 2 liters per minute instead of 3? This
means that each minute the volume of liquid in the tank will increase by 1 liter. How
does that affect the initial value problem from part (a)?
enough so it doesn't overflow.)
(Assume the tank is large

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Example: A tank initially contains 800 gallons of fresh water. Water containing 1/2 lb/gal of salt flows into the tank with the rate 6 gal/min and the well stirred mixture flows out at the rate of 2 gal/min. Write the initial value problem for Q(t), the amount of salt in pounds in the tank.
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