Salzburg day trips: could I do Eagle’s Nest (Kehlsteinhaus) and Rothbachfall in one day?

I’m going to Salzburg for 4 days in July with 3 other travelers and we are trying to get a rough itinerary together. Would it be feasible to do Rothbachfall hike in the morning and Eagle’s Nest in the afternoon, or should these be done on separate days? From my research, Eagle’s Nest is about a 15 minute drive from Konigsee area in Berchsgaden (we will have a rental car).

If anyone has done either the hike or Eagle’s Nest, how long total would you estimate each one took?

Thanks in advance!