00:01
The question says that a tank with capacity of 700 gallon initially contained 10 lb of salt dissolved in 100 gallon of water and at t equal to zero there's a solution containing 0 .5 lb of salt per gallon okay flows at the rate of 3 gallon per minute and then the mixture flows out of the tank with a rate of 2 gallon per minute.
00:24
We need to find out the time when the tank is full then in 400 gallon of 3.
00:31
Solution what will be the concentration of salt and what will be the concentration of salt once the tank is put okay so we need to form first a differential equation for the amount of salt okay so to make a differential equation okay that we are going to make a differential equation for amount of salt okay for a amount of salt in the mixture.
01:10
So let us see how can we find out.
01:12
So you see if i let here, so first i will find out what will be the rate of inflow.
01:22
So rate of inflow of salt.
01:27
So with what rate it is entering the tank, let us see that.
01:31
So it is given that at t equals to zero, the mixture containing 0 .5 lb of salt.
01:35
So 0 .5 lb per gallon okay it is entering and the gallon is entering at the rate of three gallon per mixture sorry mixture is entering at the rate of three gallon per minute per minute okay so net rate of entering of salt will be this much so this is equals to 1 .5 lb per minute so this is the net rate and outflow rate if i write outflow rate of salt in the mixture so so it will be how much.
02:08
So it has been given that initially it contains 10 lb of salt, dissolved in 100 gallon of water.
02:13
So i considered here, let the amount be y in 100 gallon of the solution...