To solve this particular problem... Work is force times displacement, and change in kinetic energy is equal to work. Think about the initial and final kinetic energies for the falling mass, and set that equal to the work done by the variable forces.
Are you in a calc based physics class, or an algebra based class? And do you have an understanding of conservation of energy yet? Or just work = force x displacment?
Looks like you and the book are correct. I would assume that the book is answering the question to 2 significant figures, thus 115.668km/h is 120km/h assuming your math is correct.