A 500 litre tank in which chocolate milk is being mixed contains 460 litres of milk and 40 litres of chocolate syrup initially. Syrup is added to the tank at the rate of 2 litres per minute and milk is added at 8 litres per minute. The syrup and milk is kept thoroughly mixed and the mixture is removed from the tank at the rate of 10 litres per minute. The amount of syrup in the tank (in litres) is denoted by S and the time (in minutes) is denoted by t. assuming perfect mixing of the milk and syrup, find an expression S in terms of t.
2006-08-31 05:34:33 · 2 answers · asked by tidus07 2 in Science & Mathematics ➔ Mathematics
The differential equation is
Change in Syrup = Input - Output
dS/dt = 2 - S*10/500
The answer is S = 100 - 60 e^(-.02t)
2006-08-31 06:03:45 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Not exactly sure what you're looking for.
If you mean the total amount of S in the tank at any time t, it's time independent and equal to the initial condition for S at t=0
If it's total S used at time t then it's just 2t+t0 (where t0 is the initial boundry condition for S0 at t0)
Doug
2006-08-31 12:44:00 · answer #2 · answered by doug_donaghue 7 · 0⤊ 2⤋