posted by bryant on .
A government agency has a current staff of 5000, of whom 25% are women. Employees are quitting randomly at the rate of 100 per week. Replacements are being hired at the rate of 50 per week, with the requirement that half be women.
Interested in the rate of women coming in and out.
Set up a differential equation to the model the situation.
My first mistake I'm guessing was thinking about this like a mixture problem. The answer is dW/dt = 25 - 2W/(100 - t).
Can someone explain to me the thought process? I have no idea where the 't' comes from and why 100 is being subtracted by it. The 2W as well I have no idea about.