Difference between 正在 and 在?
For what you are asking 在 and 正在 are basically interchangeable.

You will rarely hear 正在 in colloquial, normal, conversation - it is quite formal and elaborate. For instance looking up 你正在干什么？ gives a result from Google Books reading:


  此时你正在干什么？


No one would really talk like this unless you're playing a role in an old-timey kind of show or something like that.

在 you could contest is an abbreviation of 正在 in your given scenario and is the most down-to-earth way to express something currently being underway.