To find the average speed over the entire trip, we need to find the total distance traveled and the total time taken.
Let's assume the distance from A to B is d.
So, the distance from B to A will also be d.
The time taken to travel from A to B can be calculated using the formula: time = distance / speed.
The time taken to travel from B to A can be calculated using the same formula: time = distance / speed.
Using these formulas, the time taken to travel from A to B is t1 = d / 4.90.
And the time taken to travel from B to A is t2 = d / 2.70.
The total time taken for the entire trip is the sum of t1 and t2: t_total = t1 + t2.
The total distance traveled is the sum of the distances from A to B and from B to A: total distance = d + d = 2d.
The average speed is given by the formula: average speed = total distance / total time.
Substituting the values, we get the average speed: average speed = 2d / (d / 4.90 + d / 2.70).
Simplifying this equation, we get: average speed = 2d / ((2.70*d + 4.90*d)/ (4.90*2.70)).
Simplifying further, we get: average speed = (4.90*2.70*2d) / (2.70*d + 4.90*d).
The d term cancels out, and we are left with: average speed = (4.90*2.70) / (2.70 + 4.90).
Evaluating this expression, we find that the average speed over the entire trip is approximately 3.30 m/s.