Average Speed

Let the distance between Bandung and Jakarta be $'x'$ . So time for first half of journey is $x/20$ and that for second half is $x/30$ . ( as $\color{#3D99F6}{\small{Time=\dfrac{distance }{speed}}}$ ).

Thus, $Average ~Speed=\dfrac{Total~distance~travelled}{Total~time~taken}\\=\dfrac{2x}{\frac{x}{20}+\frac{x}{30}}\\=\dfrac{2}{\frac{1}{20}+\frac{1}{30}}=\boxed{24}$

For problem like this, I usually use an example. For example, the distance between Bandung and Jakarta is $120 km$ . On the trip from Bandung to Jakarta, I spent $\frac{120 km}{20 km/h} = 6$ hours. On the trip from Jakarta to Bandung, I spent $\frac{120 km}{30 km/h} = 4$ hours. The total time I spent is $6$ hours $+ 4$ hours $= 10$ hours. The total distance I spent from Bandung to Jakarta and from Jakarta to Bandung is $2 \times 120 km$ = $240 km$ .

So, the average speed is $\frac {240 km}{10 hours} = \boxed{24} km/h$

Please give me a better solution (algebraic) Thank you