The formula for average speed is :

(Total distance traveled)/(Total time taken)

Let’s denote the distance between Station A and Station B as d kilometers.

1. Time to travel from Station A to Station B:
   $t_1=\frac{d}{80} hourst\_1\; =\; \backslash frac\{d\}\{80\}\; \backslash text\{\; hours\}$

1. Time to travel from Station B to Station A:
   $t_2=\frac{d}{60} hourst\_2\; =\; \backslash frac\{d\}\{60\}\; \backslash text\{\; hours\}$ 
2. Total distance traveled for the round trip:Total distance = d+𝑑=2𝑑 kilometers 
3. Total time taken for the round trip:
   $Total time=t_1+t_2=\frac{d}{80}+\frac{d}{60}\backslash text\{Total\; time\}\; =\; t\_1\; +\; t\_2\; =\; \backslash frac\{d\}\{80\}\; +\; \backslash frac\{d\}\{60\}$ 
4. To add these two fractions, we need a common denominator:
   $\frac{d}{80}+\frac{d}{60}=\frac{3d}{240}+\frac{4d}{240}=\frac{7d}{240}\backslash frac\{d\}\{80\}\; +\; \backslash frac\{d\}\{60\}\; =\; \backslash frac\{3d\}\{240\}\; +\; \backslash frac\{4d\}\{240\}\; =\; \backslash frac\{7d\}\{240\}$ 
5. So, the total time for the round trip is:
   $=\frac{7d}{240} hours$
   

Average speed for the round trip:

$Average speed\frac{}{}=\frac{2d}{}\frac{7d}{240}=\frac{2d\times 240}{7d}=\frac{480d}{7d}=\frac{480}{7}\approx 68.57 km/h\backslash text\{Average\; speed\}\; =\; \backslash frac\{\backslash text\{Total\; distance\}\}\{\backslash text\{Total\; time\}\}\; =\; \backslash frac\{2d\}\{\backslash frac\{7d\}\{240\}\}\; =\; \backslash frac\{2d\; \backslash times\; 240\}\{7d\}\; =\; \backslash frac\{480d\}\{7d\}\; =\; \backslash frac\{480\}\{7\}\; \backslash approx\; 68.57\; \backslash text\{\; km/h\}$

So, the train’s average speed for the entire round trip is approximately  68.57 km/h.

There is also a shortcut formula:

• When distance is constant:
  • Consider 2 different speeds x kmph and y kmph (units can be different but should be same for x and y).
  • Since both speeds cover the same distance d. The average speed is

$\frac{2\mathrm{xy}\mathrm{}}{\mathrm{x+y}}$