Work is force applied to an object over a given distance. In this question, the librarian applies work of 1.15 m * 2.2 kg * 9.8 m/sec² against gravity to lift the book from the floor. In carrying the book 8.5 m to the stacks, the librarian does no work on the book. The librarian's muscles may be doing internal work to maintain the force necessary to hold the book up against gravity and in overcoming various internal frictional forces and inefficiencies in moving the book from one point to the other, but this doesn't count. At the stacks, the book is then lowered to a height of 0.35 m. The book now does work on the librarian, returning part of the potential energy to the librarian. The total work the librarian has done on the book is the same as if the book had already been on the floor in front of the stack and the librarian had merely picked it up and placed it on the shelf from that location, namely, 0.35 m * 2.2 kg * 9.8 m/sec², or 7.5 joules.
