Is it considered bad if a student replies late to a professor?
Firstly, take a deep breath. You are fine. I know it's hard, but try not to overthink the situation
There is no &quot;normal&quot; or &quot;expected&quot; response time set by the laws of academia (those don't exist). Sixty hours is a perfectly fine response time, especially if the email from the professor was giving lots of detailed information which you needed to think about before answering, or as you say, you needed to make progress and report on it. Email is not instant messenger and should not be treated as such. Many people in academia only check their email once a day, so wouldn't notice a &quot;slow&quot; reply at all. Furthermore, as a recipient, I'd rather get a slow, correct response than a hasty one with mistakes.
If you are worried about this in the future, it's fine to ask the professor how quickly they would like you to respond to emails. In my new job, my bosses and I discussed this openly, in fact. We decided that a week is a good maximum response time, excluding holidays. It's good to have these honest conversations about expectations for any collaboration, and it's not too late for you to do the same.
Another option is to reply to the professor's email soon after you have seen it (not interrupting your work or concentration, of course) to let them know that you have read it and are working on it and will reply with a full answer tomorrow/next week/other timeframe. However, I think this could be a bit redundant (the sender will probably assume it anyway), it unwantedly adds to the sender's email traffic and is bad for the environment.
In summary, try not to worry and don't think of email as being like Whatsapp. It's more like sending a physical letter.