Let me start of by specifying the question:
A and B are two towns. Kim covers the distance from A to B on a scooter at 17Km/hr and returns to A on a bicycle at 8km/hr.What is his average speed during the whole journey.
I solved this problem by using the formula (since the distances are same):
$$ \text{Average Speed (Same distance)} = \frac{2xy}{x+y} = \frac{2\times17\times8}{17+8} =10.88 \text{Km/hr}$$
Now I actually have two questions:
Q1- I know that $$ Velocity_{Average}= \frac{\Delta S }{\Delta T} $$ Now here does $$\Delta S$$ represent $$ \frac{S_2+S_1 }{2} \,\text{or}\, S_2-S_1 ?$$
Where S2 is the distance covered from point A to point B and S1 is the distance covered from point B to point A
Q2. How did they derive the equation: $$ Velocity_{Average(SameDistance)} = \frac{2xy}{x+y} $$
Could anyone derive it by using $$ Velocity_{Average}= \frac{\Delta S }{\Delta T} $$