Differenial Equaitions Mixing Problem You have a 5 gallon fresh water fish tank,

Question

Differenial Equaitions

Mixing Problem You have a 5 gallon fresh water fish tank, which you have not cleaned in a while, and the water looks pretty cloudy (it should be clear). You take a sample and determine that there is 50 grams of pollutant per gallon of water. A healthy tank should have less than 10 grams of pollutant per gallon and you decide your goal is to get to 5 g of pollutant per gallon. Initially there is 4 gallons of water in the tank. To not shock your poor fish, you decide to dilute the pollutant by adding 1 gallon of clean water every 30 minutes and drain the mixed water at the same rate. (a) At this rate of putting water in and taking water out at the same rate, how long does it take to reach a pollutant level of 5 g/gal? Be sure to define all variables in a table! i. When is the tank full? You return after 4 hours. How much water is on the floor?

Explanation / Answer

(a)

4 gallon water and 200 gram pollutant

After 30 min

5 gallon water and 200 gram pollutant - 40 gram pollutant per gallon

After 60 min

4 gallon water and 160 gram pollutant - 40 gram pollutant per gallon

After 90 min

5 gallon water and 160 gram pollutant - 32 gram pollutant per gallon

After 120 min

4 gallon water and 128 gram pollutant - 32 gram pollutant per gallon

After 150 min

5 gallon water and 128 gram pollutant - 25.6 gram pollutant per gallon

After 180 min

4 gallon water and 102.4 gram pollutant - 25.6 gram pollutant per gallon

After 210 min

5 gallon water and 102.4 gram pollutant - 20.48 gram pollutant per gallon

After 240 min

4 gallon water and 81.9 gram pollutant - 20.48 gram pollutant per gallon

Similarly rest as show in the table

So after 11 hours, the levels reaches to less than 5 gm pollutant per gallon

min water pollutant total pollutant per gallon 0 4 200 50.00 30 5 200.0 40.00 60 4 160.0 40.00 90 5 160.0 32.00 120 4 128.0 32.00 150 5 128.0 25.60 180 4 102.4 25.60 210 5 102.4 20.48 240 4 81.9 20.48 270 5 81.9 16.38 300 4 65.5 16.38 330 5 65.5 13.11 360 4 52.4 13.11 390 5 52.4 10.49 420 4 41.9 10.49 450 5 41.9 8.39 480 4 33.6 8.39 510 5 33.6 6.71 540 4 26.8 6.71 570 5 26.8 5.37 600 4 21.5 5.37 630 5 21.5 4.29 660 4 17.2 4.29

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.