A 30-gallon tank initially contains 15 gallons of salt water containing 2 pounds of salt. Suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. How much salt is in the tank when the tank is full? (Enter the exact numerical answer as a decimal. Do not enter a calculation.)
A 30-gallon tank initially contains 15 gallons of salt water containing 2 pounds of salt. Suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. How much salt is in the tank when the tank is full? (Enter the exact numerical answer as a decimal. Do not enter a calculation.)
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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1. Application Diff eq problem related to tank
a. A 30-gallon tank initially contains 15 gallons of salt water containing 2 pounds of salt. Suppose salt water containing 1 pound of salt per gallon is pumped into the top of the tank at the rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. How much salt is in the tank when the tank is full? (Enter the exact numerical answer as a decimal. Do not enter a calculation.)
b. A 50 gallon tank initially contains 10 gallons of fresh water. At t=0t=0 a brine solution containing 1 pound of salt per gallon is poured into the tank at the rate of 4 gal/min., while the well-stirred mixture leaves the tank at the rate of 0.5 gal/min. Find the amount of salt in the tank at the moment of overflow. Enter answer as numerical decimal correct to two decimal places in terms of pounds.
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