What is the average speed of a train if it travels the first half of the trip at 6 km/hr and the second half at 13 km/hr?

The total distance travelled by the object in a given time interval is the average speed. A scalar quantity is an average speed. It is represented by the magnitude and lacks direction.

Given:

The train covers the first half of the distance at 6 kmph and the second half of the distance at 12kmph.

When distance is equal, the Average speed = $\frac{[2\times {\mathrm{x}}_1\times {\mathrm{x}}_2]}{[{\mathrm{x}}_1+{\mathrm{x}}_2]}$ 

Average speed $=\frac{(2\times 6\times 12)}{(6+12)}$

                          = 8 km/h