a tank initially holds 100 gallons of brine solution. at t=0, fresh water is poured into the tank at teh rate of 5 gpm, while the well-stirred mixture leaves the tank at the same rate. after 20 minutes, the tank contains 20/e lbs of salt. find the initial concentration of the brine solution inside the tank.

Answer: 0.20 lb/gal

Question

a tank initially holds 100 gallons of brine solution. at t=0, fresh water is poured into the tank at teh rate of 5 gpm, while the well-stirred mixture leaves the tank at the same rate. after 20 minutes, the tank contains 20/e lbs of salt. find the initial concentration of the brine solution inside the tank.

Answer: 0.20 lb/gal

lgbasallote · Answer

if it helps the formula is $$\huge \frac{dQ}{dt} = r_1c_1 + r_2[\frac{Q}{V_o + (r_2-r_1)t}]$$
i think...

lgbasallote · Answer

hmm...im thinking

V = 100 gallons
r1 = 5 gpm
r2 = 5 gpm
at t = 20, Q =  20/e lbs

req'd c1

am i right?

hba · Answer

t=0 dt=20 min

lgbasallote · Answer

dt = 20 min? why?

lgbasallote · Answer

do i evaluate the equation at t = 20?

hba · Answer

because dt=change in time

lgbasallote · Answer

$$\large \frac{dQ}{dt} = (5)c_1 + 5[\frac{\frac{20}{e}}{10 + (0)(20)}]$$

lgbasallote · Answer

ohh you got dt from t_2 - t_1?

hba · Answer

yeah

hba · Answer

but t=0 the thing u jus solved has a problem that in there u put t=20 its 0

lgbasallote · Answer

@hba if t = 0 then what will  be Q?

mathslover · Answer

It seems to be an easy question ..--> false wait !! let me think abt this

lgbasallote · Answer

lol

mathslover · Answer

Hmn i am trying to do that : will these examples work ? http://fredmath.net/DifferentialEq/lecture1/sec1.5/sec-1.5.pdf

lgbasallote · Answer

if they did i wouldnt have asked now would i :p lol