A train travels between 2 stations X and Y.While travelling from station X to Y, it's average speed was 72 km/h.While coming back from station X and Y it's average speed was 63 km/h.Find it's average speed throughout the journey?

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Dear Student,

Average speed = $\frac{Total dis\tan ce}{Total time}$

Now, let the distance between X and Y be 'a' m. As the distance will not change during the journey from the two points. Therefore, total distance covered = 2a km.

Now let the total time taken for the journey be = t hr

So,

Avg Speed = $\frac{2a}{t}$
​​​​​
We know that,  
Speed = $\frac{dis\tan ce}{time}$
Case 1, from X to Y

Time = distance/speed
t = x/72 hr

Case 2, from Y to X

Time = distance/speed
t = x/63 hr

Therefore, total time taken
$$\begin{gathered} = \frac{x}{72} + \frac{x}{63} \\ =\frac{7x + 8x}{504} \\ = \frac{15x}{504} \\ = \frac{5x}{168} \end{gathered}$$

Now using equation 1, 

Avg speed = $$\begin{gathered} = \frac{2x}{{\displaystyle \frac{5x}{168}}} \\ = \frac{2x \times 168}{5x} \\ = 67.2 Km/hr \end{gathered}$$
Therefore, its average speed throughout the journey was 67.2 Km/h





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