1) Homer Simpson’s new swimming pool holds 10,000 gallons of water. He accidentally drops a shipment of 2000 pounds of chlorine into the water. There must be between 100 pounds and 200 pounds of chlorine in the pool for swimmers to use it. If there is too little chlorine, then algae will grow. If there is too much chlorine, then it can burn swimmers’ eyes. Homer decides to pump in pure water at a rate of 100 gallons per minute. He pumps water out at the same rate (and into Ned Flander’s yard). Assume that perfect mixing occurs.   Find an equation to determine the amount of chlorine in the pool at any given time.   How long will Bart and Lisa have to wait to use the pool?   If Homer falls asleep right after hooking up the pumps, how long can he sleep before there is not enough chlorine in the pool to prevent algae from growing?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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1) Homer Simpson’s new swimming pool holds 10,000 gallons of water. He accidentally
drops a shipment of 2000 pounds of chlorine into the water. There must be between 100 pounds and 200 pounds of chlorine in the pool for swimmers to use it. If there is too little chlorine, then algae will grow. If there is too much chlorine, then it can burn swimmers’ eyes. Homer decides to pump in pure water at a rate of 100 gallons per minute. He pumps water out at the same rate (and into Ned Flander’s yard). Assume that perfect mixing occurs.
 
Find an equation to determine the amount of chlorine in the pool at any given time.
 
How long will Bart and Lisa have to wait to use the pool?
 
If Homer falls asleep right after hooking up the pumps, how long can he sleep before there is not enough chlorine in the pool to prevent algae from growing?
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