Doing two summer research internships at the same time?
Based on my experience in math in the U.S., you should probably give up one of them. The point is not &quot;can you do the work?&quot;, but that such internships have a broader point that is not just some task. The people would want you to really engage, more fully than the allocated hours and salary might indicate, with their projects. That is, it's almost surely not just about getting some task completed, but about a mutually beneficial experience, where you'd get more than just salary, and they'd cultivate a future collaborator. &quot;Dividing by two&quot; is not palatable here.
(For example, if someone told me they wanted to work on a PhD with me, while also doing something else full time (!?!?!), I'd almost surely refuse, on the grounds that it'd just be a source of infinite frustration for me... And, in particular, a very bad investment of my mental energy.)
So, no, don't try to do both.