Chapter 10.3 Puzzle

This assignment is due 48 hours after the Chapter Test is given.

• Puzzle solutions are due by 5:00 PM two days after the Chapter Test.
• Puzzles are worth 10 points of extra credit each.
• Answers must be accompanied by valid reasoning. Just like the tests, the answer alone isn't enough!
• Please enter your solution in the text area at the bottom of this page. DON'T FORGET TO GIVE YOUR NAME!

It is the first day of your summer job at the local kiddie pool with silly slides. After cleaning all the dead leaves out of the pool you slowly fill it up with 10,000 gallons of clean water. Your last chore for the day is to add the required four pounds of chlorine granules. Or is it two pounds? Checking the instructions left for you by the pool boss you realize you've added twice the legal amount of chlorine to the pool!

(1) You decide to open the drain to let water flow out of the pool, while adding fresh water to keep the volume constant. The water drains out at a rate of 12 gallons per minute. Assuming that the water in the pool stays well mixed, write a differential equation for dC/dt, where C is the amount of chlorine granules in the pool, measured in pounds, and t is time, measured in minutes.

(2) It is 5:30 PM now. Do you have time to get the chlorine concentration down to the correct level before the pool opens tomorrow at 8 AM or will you be fired?

(3) Suppose the "clean" water you are adding actually contains 0.00005 pounds of chlorine granules per gallon of water. How does this affect your answer to Question (2)? You can assume that the water originally in the pool (before you added anything) was completely chlorine-free.

Don't forget to explain your answer as clearly as possible.

Please type LAST name:

Please type your Student ID Number:

I received no help from anyone on this assignment.