Hi, I think I have the correct solution to your problem.
Let A be the point at the top of the hill.
Let B be the point at the base of the hill.
Let C be the final point where the cyclist stops.
At A, PE=80*g*4=320g J, since sin(theta)=height/80=1/20, so height=4.
KE=0.
TOTAL ENERGY=320g J.
At B, PE=0
KE=1/2*80*v^2
TOTAL ENERGY= 40v^2.
The work done in going from A to B is Fd=80F N
Hence 320g=40v^2+80F. (1)
NEXT
The TOTAL ENERGY at B is 40v^2 J,(as before)
At C, the PE=0
KE=0
The Work done in going from B to C is Fd=80F N.
Hence 40v^2=0+80F
Substituting this into expression (1), gives
320g=80F+80F
Hence the resistive force F=2g N.
Hope this helps.