Question

A 100 gallon tank is filled with a salt solution containing 10 lbs of salt. Pure water is pumped in at a rate of 5 gallons per minute and pumped out at the same rate. How many minutes will it take the amount of salt to drop to 8 lbs? Round to one decimal place.

Answer 1

see the related questions below. They should help you set up and solve your differential equation.

If you get stuck, come back with what you have done so far.

Answer 2

I keep getting an negative answer. I know the answer is 4.5 only because the teacher tells us what it I just cannot figure out how to set it up. I got e^t/20 +1/20Ae^t/20 = 5e^t/20, which is way wrong

Answer 3

check to see how much salt is coming in and going out. Since pure water contains no salt, and the 5 gallons leaving contain 5/100 of the salt present, we have

ds/dt = 5/100 * 0 - 5/100 s
ds/dt = -1/20 s
ds/s = -1/20 dt
s = c*e^(-t/20)
Since s(0) = 10,
s = 10*e^-(t/20)

so, let's find t when s=8

10 e^(-t/20) = 8
e^(-t/20) = 0.8
-t/20 = ln0.8
t = -20 ln0.8 = 4.46

Looks like you need to review the logic that led to your original DE.

Answer 4

Thanks (:
I knew it had t/20 in the solution somehow. I see what I did wrong now.