ok, i found this game that is so work friendly. it is fish tycoon. you raise and sell fish and it is all in real time. so you can maintain your game and let it run itself while you work.
on the bottom left of the screen there is a little shell that says "supplies". click on that and then you have $200. you can get the cheep fish eggs. you put them in the water and then you have fish. there is a jar at the top that is unmarked that is growth hormone. you have 3 drops so i wouldn't use it all on one batch of fish, but you can speed the growth process a little. you can also speed it up by going to menu and then options.
if you have it on fast it takes like an hour. i know it takes a long time, but that is what i liked about it so much. because you can leave it and do a bunch of work or eat or whatever and come back to it and you have grown fish or babies or whatever and it it continues overnight so you can pick up when you come back in to work in the morning.