Power question?

Question

A 1900 kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down a hill at 27 m/s. Going up a hill, the car's engine needs to produce 47 horsepower more power to sustain the constant velocity than it does going down the same hill. At what angle is the hill inclined above the horizontal?

Answer 1

Pf=friction power, Pg=grav. power
Pf+Pg = 47hp + Pf-Pg
Pg = 23.5 hp
Convert Pg to watts
Pg = VF = Vmgsinθ
θ = arcsin(Pg/(Vmg))