Thread: when is the tank empty?

a large tank is filled to capacity with 500 gallons of pure water. brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gal/min. the well mixed solution is pumped out at 10 gal/min. find the number A(t) of pounds of salt in the tank at time t.

ok so I know dA/dt = rate in - rate out.

so dA/dt = (2 lbs/gal)(5 gal/min) - ()???

ok im stuck with how to figure out the rate out?

my book is saying the rate out = 2A/(100-t)??? i dont see how the book came up with that answer...any thoughts?

thanks in advance....

Rate out = (A/(total amount of liquid in gallons present at time t)) * (10 gal/min). The total amount of liquid is changing by a net amount of 5 gallons per minute, since the rate out is greater than the rate in. So you have (A/(500-5t))(10)=2A/(100-t). Voila.

yea i think i need to practice more of these problems...thanks again.

You're welcome, as always.