On fractional equation If a person's speed from a to B is a and that from B to a is B, then his average speed from a to B is () (2ab)/(a+b)

On fractional equation If a person's speed from a to B is a and that from B to a is B, then his average speed from a to B is () (2ab)/(a+b)

Let the distance between a and B be X
Then the speed from a to B is a and the time is x / A
The speed from B to a is B and the time is x / b
The total distance to and fro is 2x, and the total time to and fro is (x / a) + (x / b)
So the average speed is
2x÷(x/a+x/b)
=2x÷[(ax+bx)/ab]
=2x×ab/x(a+b)
=2ab/(a+b)