Mixing problem (differential equation)
A tank is filled with 1000 liters of pure water. Brine containing 0.05 kg of salt per liter enters the tank at 7 liters per minute. Another brine solution containing 0.08 kg of salt per liter enters the tank at 10 liters per minute. The contents of the tank are kept thoroughly mixed and the drains from the tank at 17 liters per minute. A. Determine the differential equation which describes this system. Let S denote the number of kg of salt in the tank after t minutes. Then [dS/dt] = ?
B. Solve the differential equation for S(t). S(t) =
For part A., I got dS/dt = (1150-S)/1000.
For part B., I got S(t) = -1150e^(-t/1000)+1150.
Apparently at least one of these is not right, but I don't know why. Please help.