It's a tricky sentence really, and I honestly cannot tell you exactly why, but my best guess, as a Danish person, would be that: "arbejdet" means that specific job or work place, whereas "arbejde" would just mean some job that he's working at, but we don't know which one. This is not conveyed in the English sentence, since it would sound rather silly.
In this case I think you should report 'my answer should be accepted', because the most natural English or Danish translations are always the best, as long as they mean the same thing as is intended. Eg. saying 'he takes (his) breakfast to work' might have the same implication (that he eats it at work) but not the same exact meaning. Your translation does have the same meaning so if you think it's more natural you aim for that.