Question

A 24 gallon tank is filled with pure water. Water which has a concentration of 6g...

A 24 gallon tank is filled with pure water. Water which has a concentration of 6g of salt per gallon flows into the tank at a rate of 2 gallons/min, and the mixture is stirred to a uniform concentration. Water also leaks from the tank at the same rate, 2 gallons/min.

Find a differential equation describing the rate of change of salt in the tank.

Hint: The concentration of salt in the tank is S(t)/24, where S(t) is the total amount of salt in the tank at time t, in grams. S′(t), the rate of change of salt in the tank over time, is equal to the [rate in] − [rate out]
Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A tank initially contains 120 L of pure water. A mixture containing a concentration of 9...
A tank initially contains 120 L of pure water. A mixture containing a concentration of 9 g/L of salt enters the tank at a rate of 3 L/min, and the well-stirred mixture leaves the tank at the same rate. Determine the differential equation for the rate of change of the amount of salt in the tank at any time t and solve it (using the fact that the initial amount of salt in the tank is 0g).
A tank contains 300-gallon of pure water. At time t = 0, a solution containing 2...
A tank contains 300-gallon of pure water. At time t = 0, a solution containing 2 lb of salt per gallon flows into the tank at a rate of 1 gallon per minute, and the well-stirred mixture flows out at a rate of 2 gallons per minute. Find the amount(in lb) of salt Q in the solution as a function of t in minutes. please show work and explain thank you
Using differential equation: A 200- gallon tank initially contains 40 gallons of brine in which 10...
Using differential equation: A 200- gallon tank initially contains 40 gallons of brine in which 10 pounds of salt have been dissolved. Starting at t=0 , brine containing 5 pounds of salt per gallon flows into the tank at rate of 6 gallons per minutes. At the same time, the well-stirred mixture flows out of the tank at the slower rate of 4 gallons per minute. a)How much salt is in the tank at the end of t minutes? b)...
Consider a 400-gallon capacity tank of water that contains 200 gallons of water in which 10...
Consider a 400-gallon capacity tank of water that contains 200 gallons of water in which 10 pounds of salt are dissolved. Suppose that water with a salt concentration of 2 pounds per gallon enters the tank at a rate of 6 gallons per minute, is well-stirred, and the mixture leaves the tank at 9 gallons per minute. Set up and solve the initial value problem to get the amount of salt as a function of time. Use this function to...
A large 500 gallon tank is full of pure water. Brine comes in that has 2...
A large 500 gallon tank is full of pure water. Brine comes in that has 2 (lb) of salt per gallon and a ratio of 5 (gal / min). The well mixed solution selling the tank with the same reason. a) determine the amount A(t) of pounds of salt in the tanqye at time t b) What is the concentration c(t) of salt in the tank at time t? And at time t = 5min? What is the concentration in...
A 50-gallon tank initially contains 10 gallons of fresh water. At t = 0, a brine...
A 50-gallon tank initially contains 10 gallons of fresh water. At t = 0, a brine solution containing 2 pounds of salt per gallon is poured into the tank at a rate of 5 gal/min. The well-stirred mixture drains from the tank at a rate of 3 gal/min. Find the amount of salt in the tank at the moment of overflow. Please use differential equations to solve this problem and please put the answer in decimal form. I did this...
Consider a 2500-gallon capacity tank of water that contains 100 gallons of water in which 10...
Consider a 2500-gallon capacity tank of water that contains 100 gallons of water in which 10 pounds of salt are dissolved. Suppose that water with a salt concentration of 2 pounds per gallon enters the tank at a rate of 6 gallons per minute, is well-stirred, and the mixture leaves the tank at 5 gallons per minute. (a) Set up and solve the initial value problem to find the amount of salt in the tank as a function of time....
A tank is filled with 10 gallons of brine in which is dissolved 5 lb of...
A tank is filled with 10 gallons of brine in which is dissolved 5 lb of salt. Brine containing 3 lb of salt per gallon enters the tank at a rate of 2 gal per minute, and the well-stirred mixture is pumped out at the same rate. (a) Find the amount of salt in the tank at any time t. (b) How much salt is in the tank after 10 minutes? (c) How much salt is in the tank after...
A tank contains 30 gallons of brine solution containing 10 lb of salt. Another brine solution...
A tank contains 30 gallons of brine solution containing 10 lb of salt. Another brine solution of concentration of 3 lb/gallon is poured into the tank at the rate of 2 gallons/min. The well stirred solution in the tank is drained out at the rate of 2 gallons/min. Let the amount of salt in the tank at time ? be ?(?). Write the differential equation for A(t) and solve it.
A 100 gallon tank is filled with brine solution containing 50 pounds of salt. Pure water...
A 100 gallon tank is filled with brine solution containing 50 pounds of salt. Pure water enters the tank a rate of 10 gal per hour. Well mixed solution leaves the first tank at the same rate (10 gal/hr) and enters a second 100 gallon tank initially containing 10 pounds of salt. How much salt is in tank 2 at any time?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT