thx! A tank contains 200 gallons of water. Five gallons of brine per minute flow

Question

thx!

A tank contains 200 gallons of water. Five gallons of brine per minute flow into the tank, each gallon of brine containing 1 pound of salt. Five gallons of water flow out of the tank per minute. Assume that t he tank is kept well stirred. Find a differential equation for the number of pounds of salt in the tank (call it y say). Assuming the tank intially contains no salt, solve this differential equation. At what time will there be 100 lbs of salt in the tank? (give an exact answer and a numerical answer accurate to two decimal places.

Explanation / Answer

V = 200+ 5t - 5t = 200 = constant

y = VC0 + (5*1 - 5*C )t

dy/dt = 5(1-C)

y= VC = 200C

200dC/dt = 5(1-C)

ln(1-C) = -t/40 +c

at t = 0

C = 0

=> c = 0

C = 1-e^(-t/40)

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