A driver travels three-fourth distance of his journey at a velocity (v) and completes rest of the journey at one half of his original velocity (½v). What was his average speed for the trip?
Let us say the total travel distance is D.
So then `3/4D ` of the distance is travelled under velocity v and the rest `1/4D` is travelled under velocity `1/2v` .
Time for travel at `v` speed `(t_1) = (3/4D)/v = (3D)/(4v)`
Time for travel under `1/2v` speed` (t_2 ) ` `= (1/4D)/(1/2v) = D/(2v)`
Average speed = (total distance)/(total time)
Average speed `= D/(t_1+t_2)`
Average speed `= D/((3D)/(4v)+D/(2v))`
Average speed `= D/((5D)/(4v))`
Average speed `= 4/5v`
Average speed `= 0.8v`
So the answer is 0.8v. The correct answer is at .