I don't remember exactly how long it took. Looking at photo timestamps from my hike last year.. I was at Whitney summit at 12:10 (via MR) and then have a pic of us scrambling up the lower part of the Mt. Muir rocks at 1:10 and then a selfie at the top with the registry at 1:32. It took us a while to decide whether or not to go up due to 50mph+ gusts of wind and the exposed scramble. I ended up climbing up to the summit block alone, climbing down, and then going up a second time with a friend. I'd estimate at the trail intersection you are ~1hr from Whitney summit and 20-30 min from Muir summit. That's just an estimate though.
Keep in mind - the climb up to the top of Muir seemed to me like a class 3+ with moderate exposure. There are a few sections where you really don't want to fall. Unremarkable summit block, but it feels good to top out.
