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At time t = 0 a large tank contains Qo solution containing 2 pounds of sugar pe per hour. The mixture is thoroughly stirr drained at the rate of 20 gallons per hou at time t. Find a differential equation tha Hint: note that the total volume of soluti gallons goes into the tank but 20 gallons

At time t = 0 a large tank contains Qo solution containing 2 pounds of sugar pe per hour. The mixture is thoroughly stirr drained at the rate of 20 gallons per hou at time t. Find a differential equation tha Hint: note that the total volume of soluti gallons goes into the tank but 20 gallons

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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10 pts At time t = 0 a large tank contains Qo pounds of sugar dissolved in 500 gallons of water. A water solution containing 2 pounds of sugar per gallon is flowing into the tank at the rate of 15 gallons per hour. The mixture is thoroughly stirred at all times. Also, the mixture in the tank is being drained at the rate of 20 gallons per hour. Let Q(t) be the number of pounds of sugar in the tank at time t. Find a differential equation that models Q(t). (Do not solve this equation.) Hint: note that the total volume of solution in the tank is not a constant 500 gallons, since 15 gallons goes into the tank but 20 gallons leaves the tank each hour.
Transcribed Image Text:10 pts At time t = 0 a large tank contains Qo pounds of sugar dissolved in 500 gallons of water. A water solution containing 2 pounds of sugar per gallon is flowing into the tank at the rate of 15 gallons per hour. The mixture is thoroughly stirred at all times. Also, the mixture in the tank is being drained at the rate of 20 gallons per hour. Let Q(t) be the number of pounds of sugar in the tank at time t. Find a differential equation that models Q(t). (Do not solve this equation.) Hint: note that the total volume of solution in the tank is not a constant 500 gallons, since 15 gallons goes into the tank but 20 gallons leaves the tank each hour.
Expert Solution
Step 1

The amount of sugar dissolved in the tank initially=Qo pounds

Volume of water in the tank=500 gallons

The rate of inflow of sugar=2 pounds/gallon

The rate of inflow of solution=15 gallons/hour

Therefore, the inflow of sugar=2×15=30 pounds/hour

The rate of outflow of mixture=20 gallons/hour

At any time , (t)the amount of sugar in the tank =Q(t)

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