For a) the average speed is ##s_a=Δx/Δt## ok.So half of the time the car goes 55 km/h let's call total trip t and total distance d so the equation will be ##55km/h.t_1+90km/h.t_1=d## , ##t_1=t/2## average speed is total distance divided by time so ##d/2t_1= 145t_1/2t_1=72.5 km/h##
For b) So half of the distance is ##d/2## so ;
##d/2=55km/h.t_1##
##d/2=90km/h.t_2##
so ##t_1/t_2=1,636## so ##t_1=t_2.1,636##
##s_a=Δx/Δt##
##s_a=d/(t_1+t_2)=180t_2/(t_2+t_2.1.636)##