Pick some distance the motorcyclist might have traveled (it doesn't matter what distance but for ease of calculation I chose 120 km).
Time spent traveling 120 km at 40 km/hr
Time spent traveling 120 km at 60 km/hr
Total time spent traveling
The answer is (b)
I want to provide an alternative approach to figuring out the average sspeed of the motorcyclist.
So, you know that the motorcyclist travels the same distance, let's say
Let's assume that it takes him
This means that you can write
#d = 40 * t_1" "#and #" "d = 60 * t_2#
This is equivalent to
#40 * t_1 = 60 * t_2 implies t_1 = 3/2 * t_2#
The average speed of the motorcyclist can be thought of as the total distance he covered divided by the total time needed.
Since he goes from
#d_"total" = 2 * d#
The total time will be
#t_"total" = t_1 + t_2#
#t_"total" = 3/2 * t_2 + t_2 = 5/2 * t_2#
The average speed will thus be
#bar(v) = (2d)/(5/2 * t_2) = 4/5 * d/t_2#
#bar(v) = 4/5 * 60 = color(green)("48 km/h")#