I'm trying to solve a textbook problem that says:

*A boy in a wheelchair (total mass 47.0 kg) has speed 1.40 m/s at the crest of a slope 2.60 m high and 12.4 m long. At the bottom of the slope his speed is 6.20 m/s. Assume air resistance and rolling resistance can be modeled as a constant friction force of 41.0 N. Find the work he did in pushing forward on his wheels during the downhill ride.*

I'm a little bit confused about what is the force that the boy is doing. I would think that he applies a force to the wheels and they apply a force to the floor which in return causes a friction force that moves the wheelchair. The conservative forces acting on the boy are the weight's Y component and the normal force, while the non-conservatives forces are friction and weight's X component. The conservative forces here don't do any work. So, if we suppose that the force exerted by the boy is the same as the friction force but in opposite direction, then we could calculate the work done by the friction force to find the work done by the boy.

Work_{friction force} = - 41 N * 12.4 m

Work_{friction force} = -504,4 J

The work done by the boy is 504 J. But I'm not sure if my answer is correct, and seeing that I'm also given the velocities, I think I should maybe do something with them. Maybe use kinetic energy calculations. But I'm not sure why that's actually necessary. What am I doing wrong?