I would imagine this was a beautiful hike. Unfortunately for us, we had a rainy, cold, windy day...in early August! Even got sleeted on at the top of First Burroughs.
Actually, when the sun popped out for a few moments, the views of the area around the Burroughs, especially back down to Frozen Lake and, in the other direction, the White River, were spectacular. But as far as Mount Rainier - it might as well not have been there, since we couldn't see any of it.
Two days later, we did the Tolmie Peak hike in gorgeous weather. Now having seen the Burroughs from that vantage point, I'd recommend this hike even without having had the best day to be on it.