A 50 gallons tank initially contains 10 gal of fresh water. At t = 0, a brine solution
containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min, while the
well-stirred mixture leaves the tank at the rate of 2 gal/min. Find
a. the amount of time required for overflow to occur
b. the amount of salt in the tank at the moment of overflow
2.
Let amount, in lb of salt at time Then we have
(rate of salt into tank) − (rate of salt out of tank)
So we get the differential equation
Integrating factor
Integrate
a.
The tank overflows at min.
b.
Comments
Leave a comment