math
posted by deel .
A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution containing 50% water and 50% alcohol is added to the tank at rate of 4 gallons per minute. As the second solution is being added, the tank is being drained at the rate of 5 gallons per minute. Assuming the solution in the tank is stirred constantly, how much alcohol is in the tank after 10 minutes?

Would it not be a similar to a previous problem?
http://www.jiskha.com/display.cgi?id=1344476111
You can try the same approach and post your attempt for a check. 
oke thanks, i'ill try it

y(t)=amount of alcohol in the tank at time t
dy/dt
=y’(t)
= alcohol inflow rate – alcohol outflow rate
= 4  5(y/50)
=200  5y/50
= 5 (40y)/50
dy/dt = 5 (40y)/50
Separate variable and integrate :
dy/(40y) = 5/50dt
ln(40y) = 0.1t + C
ln(40y) = 0.1t + C
40y= Ce^0.1t
Y= 40(1Ce^0.1t) ….. eq. 1
Initially, the tank contains 50 gallon (50% alcohol) = 25 gallon of alcohol,
y(0) = 25
substituting y=25 and t=0 in to eq.1 gives
25 = 40(1C)
2540 = 40C
C = 0.375
When t=10 minutes
y(10) = 40(10.375*e^0.1(10))
y(10) = 40(10.375*0.367)
y(10) = 34.48 gallon
at t=10’, amount of alcohol in the tank
= 50% x 34.48 gallon = 17.24 gallon or 34.48%
please correct the result of my work. thanks 
Yes, you have done a fantastic job of setting up and solving the problem.
If you reread the question carefully, you will probably discover a few traps.
If you don't find the traps, here are a few hints to improve the solution:
1. Alcohol coming into the tank is 50%, so intake rate is 4*0.5=2 gal/min.
2. Initial concentration is 90%, so initial alcohol content is 50*0.9=45 gal.
3. Initially, output volume is y/50 (as you had it).
However, since the input is 4 gal/min, and output is 5 gal/min, you will need to divide by the total volume as a function of time, which turns out to be 50t.
4. finally, do not forget required parentheses. Otherwise, your work will be very hard to read, such as:
"= 4  5(y/50)
=200  5y/50
..."
instead of
= 4  5(y/50)
=(2005y) / 50
Good job, keep up the good work. 
thanks for your help :)

You're welcome!
Respond to this Question
Similar Questions

Math/Physics
Please check my work below and comment. A tank initially contains 80 gallons of fresh water. A 10% acid solution flows into the tank at the rate of 3 gallons per minute. The wellstirred mixture flows out of the tank at the rate of … 
Math
Beginning with a tank containing 8075 gallons of gasoline, more gas is added at a rate of 5 gallons per minute, while alcohol is added at a rate of 10 gallons per minute. When the mixture is 10% alcohol, how many gallons of the mixture … 
math
Water is Pumped into an underground tank at a constant rate of 8 gallons per minute.Water leaks out of the tank at the rate of (t+1)^½ gallons per minute, for 0<t<120 minutes. At time t=0, the tank contains 30 gallons of water. … 
calculus
Water is Pumped into an underground tank at a constant rate of 8 gallons per minute.Water leaks out of the tank at the rate of (t+1)^½ gallons per minute, for 0<t<120 minutes. At time t=0, the tank contains 30 gallons of water. … 
chemical calculations
Brine from a first tank runs into a second tank at 2 gallons per minute and brine from the second tank runs into the first at 1 gallon per minute.Initially,there are 10 gallons of brine containing 20 lb of salt in the first tank and … 
linear
Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains x(t) pounds of salt in 200 gallons of brine, and tank B contains y(t) pounds of salt in 300 gallons of brine. The … 
linear algebra
Suppose that we have a system consisting of two interconnected tanks, each containing a brine solution. Tank A contains x(t) pounds of salt in 200 gallons of brine, and tank B contains y(t) pounds of salt in 300 gallons of brine. The … 
Math
One solution contains 25% as much water as alcohol and another solution contains 5 times as much water as alcohol. How many gallons of each solution must be mixed in order to obtain 7 gallons of the new solution which contains as much … 
CALC
A 200gallon tank is currently half full of water that contains 50 pounds of salt. A solution containing 1 pounds of salt per gallon enters the tank at a rate of 6 gallons per minute, and the wellstirred mixture is withdrawn from … 
Algebra
A tank contains 150 gallons of water and fills at a rate of 8 gallons per minute. A second tank contains 600 gallons of water and drains at a rate of 10 gallons per minute. After how many minutes will both tanks have the same amount …