Yeah, or perhaps, you can post from time to time say that it's getting late and the sun is going down, or that it's getting dark, etc. Not exactly the time, cause it might cause some problems we're not thinking about. Instead just say that it's Morning, Noon, Afternoon, Night, etc. and if someone needs to do something, they can just say whatever time they want.
For example:
You said it's Afternoon. So someone might put in their post: I got a call from the professor and he told me to come by his Lab at 5PM.
That is acceptable because 5PM is in the afternoon. But if he said 5AM, he wouldn't be right. Also, perhaps a posting limit? So no one gets left behind? Personally I'm not very fond of the idea myself cause I wanna post whenever I get the chance, but there are people who haven't even gotten their first pokemon yet ><