Suppose there are two tanks, each containing 20 L of fluid. Tank 1 initially contains water with 4kg of salt dissolved and Tank 2 initially contains pure water. The tanks are stirred constantly so their solutions have uniform concentration. There is a pipe which takes 15 L/min from tank 1 to tank 2, and another pipe which takes 15 L/min from tank 2 to tank 1. Also, pure water is being pumped into each of tank 1 and tank 2 at a rate of 5 L/min, and solution is being removed at a rate of 5 L/min from each of tank 1 and tank 2. Model the initial value problem as a system of two first order differential equations, solve the initial value problem, and find the amount of salt in tank 1 after one minute.

Suppose there are two tanks, each containing 20 L of fluid. Tank 1 initially contains water with 4kg of salt dissolved and Tank 2 initially contains pure water. The tanks are stirred constantly so their solutions have uniform concentration. There is a pipe which takes 15 L/min from tank 1 to tank 2, and another pipe which takes 15 L/min from tank 2 to tank 1. Also, pure water is being pumped into each of tank 1 and tank 2 at a rate of 5 L/min, and solution is being removed at a rate of 5 L/min from each of tank 1 and tank 2. Model the initial value problem as a system of two first order differential equations, solve the initial value problem, and find the amount of salt in tank 1 after one minute.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Suppose there are two tanks, each containing 20 L of fluid. Tank 1 initially contains
water with 4kg of salt dissolved and Tank 2 initially contains pure water. The tanks
are stirred constantly so their solutions have uniform concentration.
There is a pipe which takes 15 L/min from tank 1 to tank 2, and another pipe which
takes 15 L/min from tank 2 to tank 1. Also, pure water is being pumped into each
of tank 1 and tank 2 at a rate of 5 L/min, and solution is being removed at a rate of
5 L/min from each of tank 1 and tank 2.
Model the initial value problem as a system of two first order differential equations,
solve the initial value problem, and find the amount of salt in tank 1 after one minute.

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