Program Explanation Given information: The tank contains 1000 Liters of a solution consisting of 100 kg of salt dissolved in the water. The rate at which the pure water is pumped into the tank is 5 L/s . Calculation: Given that the input into the tank and output from the tank both are same that is r i = 5 and r o = 5 Now, the concentration of input is c i = 0 Then, the concentration of output is, c o ( t ) = x ( t ) V ( t ) where V ( t ) = V o + ( r i − r o ) t Given that V o = 1000 , r i = 5 and r i = 5 Then, V ( t ) = 1000 Hence, c o ( t ) = x ( t ) 1000 The differential equation of the given problem is, d x d t = r i c i − r o c o = 5 × 0 − 5 ( x 1000 ) = − 5 x 1000 = − x 200 Re-write the equation as, d x x = − d t 200 On integrating both sides, ∫ d x x = −

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

5th Edition

ISBN: 9780321816252

Author: C. Henry Edwards, David E. Penney, David Calvis

Publisher: PEARSON

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Question

Chapter 1.5, Problem 33P

Program Plan Intro

To calculate: The time till 10 kg of salt remains in the tank.

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Chapter 1.5, Problem 32P

Chapter 1.5, Problem 34P

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Chapter 1 Solutions

Differential Equations: Computing and Modeling (5th Edition), Edwards, Penney & Calvis

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The time till 10 kg of salt remains in the tank.

Solution Summary: The author calculates the time till 10kg of salt remains in the tank, and the rate at which the pure water is pumped into it.

To calculate: The time till 10 kg of salt remains in the tank.

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Chapter 1 Solutions