Calculating average velocity for this kind of motion

[CherryWine]

Homework Statement

For the first half of a straightly traveled path which is α=60° from some reference line, a body is moving with a velocity of v₁=72 km/h. During the second half of a straightly traveled path, the body is moving with an angle of β=30° with a velocity of v₂=36 km/h.What is the average velocity?

Homework Equations

All translational kinematic.

The Attempt at a Solution

So first of all I've calculated x and y components of the both velocities. Then, I've found average component velocities of the resultant average velocity needed (I've done this bearing in mind that the body is moving with one velocity for the half of the total path, and with another velocity for the second half of the total path). I've obtained the average velocity as 43.55 km/h, however the answer in the says that the average velocity would be 46.3 km/h. So if you could solve the problem yourself and tell me what you get as the result.

 

[BvU]

Tell us in detail how you found your answer. I get 46.36

 

[Irene Kaminkowa]

To be exact, it is
$$24\sqrt{2+\sqrt{3}} km/h$$

 

[BvU]

It is indeed. But the numerical value isn't all that interesting. What is important is the path toward the correct answer.
Now, dear Cherry, what did steps did you take ?