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nysnacc

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## Homework Statement

Initially 5 grams of salt are dissolved in 20 liters of water. Brine with concentration of salt 2 grams of salt per lter is added at a rate of 3 liters per minute. The tank is mixed well and is drained at 3 liters a minute. How long does the process have to continue until there are 20 grams of salt in the tank?

## Homework Equations

Rate in / Rate out

Concentration = mass / Volume

## The Attempt at a Solution

Rate in = 3L /min

Concentration in =2 g/L

rate out =3L /min

Concentration out =x g/L

I set change of concentration as x'

x' = lim Δt→0 (3 L/ min * 2 g/L *Δt - 3 L/ min * x g/L *Δt) / V *Δt

so x' = (3*2 - 3*x) / V where V =20 L (given)

x' = 3/10 - 3x/20

then use integrating factor, but I have different answer what am I doing wrong? thank