Cyclist of 80kg: Descending 3.4 degree Hill at 9.0 or 30 km/hr?

[Omanlew]

A bicylcist of mass 80 kg (including the bike) can coast down a 3.4 deg hill at a steady speed of 9.0 km/hr. Pumping hard, the cyclist can descend the hill at a speed of 30 km/hr. Using the same power, at what speed can the cyclist climb the same hill? Assume the force of air resitance is directly proportional to the speed v; that is Fsubfr=bv, where b is a constant.


Not really sure how to approach this..

 

[Dick]

When he is coasting down the hill the component of gravity along the road balances the force of air resistance at 9km/hr. Figure out what that resistance force (F_fr) actually is since F_fr+F_g=0. When he's pumping hard at 30km/hr the resistance force is 30/9 times what it used to be. If the force he is exerting at 30km/hr is F_p then you now have F_p+F_g-(30/9)*F_fr. Figure out F_p. When he's going uphill F_g reverses. What's the new resistance force? Can you use that resistance force to figure the velocity?