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A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy (kg/min) y(0) = k kg. dt (b) Solve the initial value problem in part (a) y(t) -kg. = (c) Find the amount of salt in the tank after 4 hours. = (kg) amount = (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)

A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy (kg/min) y(0) = k kg. dt (b) Solve the initial value problem in part (a) y(t) -kg. = (c) Find the amount of salt in the tank after 4 hours. = (kg) amount = (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)

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 contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy dt =(kg/min) y(0) = k kg. (b) Solve the initial value problem in part (a) y(t) =0kg. = (c) Find the amount of salt in the tank after 4 hours. amount = (kg) (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)
Transcribed Image Text:A tank contains 50 kg of salt and 1000 L of water. Pure water enters a tank at the rate 10 L/min. The solution is mixed and drains from the tank at the rate 5 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy dt =(kg/min) y(0) = k kg. (b) Solve the initial value problem in part (a) y(t) =0kg. = (c) Find the amount of salt in the tank after 4 hours. amount = (kg) (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = =(kg/L)
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