Find the average speed when the first half of a journey is done at a speed of 60 km/h and the second half at a speed of 40 km/h.

Average speed = $$ \frac{(2xy)}{(x + y)}$$

                      = $$ \frac{(2\times60\times40)}{(60 + 40)}$$ = 48 km/h

Other method :

Let the total distance be 100 km

Time taken in 1st half = $$\frac{50}{60}$$ = $$\frac{5}{6}$$

Time taken in 2nd half = $$ \frac{50}{40}$$ = $$ \frac{5}{4}$$

Total time taken in 100 km = $$ \frac{5}{4}+\frac{4}{5}= \frac{25}{12}$$

Average speed = $$\frac{Total  distance}{Total  time taken}$$

                      = $$ \frac{100}{\frac{25}{12}}=\frac{100\times12}{25}$$= 48 km/h