Thanks for the reply! Your tip helped me to get through that part of the map and I was able to complete the demo, the rest I really enjoyed.
I think the reason I got stuck is that I didn't notice that much of a difference in speed between beginning my run in the room and starting in the previous room, because I took one look at that room and figured that I had to find a way to move faster, much like how a similar room taught me to run in Super Metroid. Thanks for your help!