[From here]

Link broke into a run as soon as he crossed the threshold of the Sun Room. Even if something was waiting for them in here, there was absolutely no time to be wasted. He only made sure that Sora was still with him as he approached the door into the library.

[From here.]

Once they got inside of the library, Sora definitely slowed down. It just didn't feel like the kind of place they could run in, since libraries were always supposed to be quiet.

Besides, they were going to have to pull the switch in the bookshelf first anyway. Sora knew exactly where the Oxford book was now, so without any delay he moved over and yanked it out.

The door slid open and he turned back to Link. "Let's go."