Hi,
As far as I can tell does it mean several things:
Shigoto o shimasu = going to work
atode hirogohan o tabemasu = later, I will have dinner
nan ji ni hirugohan o tabemasu ka? = At what time do you want to have dinner?
Hope that helps!
This aforementioned translation is a bit off. But the first sentence is impossible to translate literally into English. A literal translation of this colloquial expression would be:
Around the time of now I'm working. After that I will eat lunch. What time do you eat lunch?
It's actually more like:
After I finish this up (at work, usually), I'm going to lunch. What time are you going to lunch?
Hirugohan=lunch
Yorugohan=dinner