00:01
Students, in this question we are given that the tank has 160 gallon of fresh water in which half lb of salt per gallon is poured into the tank at a rate of 4 gallon per minute and after 5 minutes the salt water switches to fresh water.
00:23
So, again at a rate of 4 gallon per minute.
00:32
Now we have to find the amount of salt in the tank.
00:36
So to find the amount of salt let us use the form ds by dt that is rate of change of the amount of salt at the time t.
00:46
So that will be equal to rate of flow which is in input and the rate of outflow.
00:56
First let us calculate the rate of inflow that will be equal to 9 into 4 which is equal to 36 lb per gallon and rate of outflow which is calculated using the salt amount in 160 gallons of fresh water into the rate of change which is 4 gallon per minute.
01:28
So that will be equal to 4 is divided by 160.
01:36
Now let us calculate ds by dt using the values which we got in rate of inflow and minus rate of outflow.
01:46
So rate of inflow we got 36 minus and here it is 4 is divided by 160.
01:54
Now this can be written as 36 minus s by 40.
02:00
Now we can rewrite this as ds by 36 into 40 minus s equal to 1 by 40 into dt.
02:18
Now integrating on both sides we will get ds divided by 100 sorry 1440 minus s equal to 1 by 40 t plus c...