# A train travels a distance of 480 km at a uniform speed. if the speed had been 8 km/h less. then it would have taken 3 hours more to cover the same distance. we need to find the speed of the train.

$\\ \text{Let the speed of the train} =x \mathrm{km} / \mathrm{hr}\\ \text{ Distance} =480 \mathrm{km}\\ \text{ Time taken by the train to cover the distance of 480}\ \mathrm{km} =\frac{480}{x} hrs\\ \text{Now, according to the given question,} \\ \begin{array}{l} \quad \frac{480}{x-8}-\frac{480}{x}=3 \\ \Rightarrow \quad 480\left[\frac{1}{x-8}-\frac{1}{x}\right]=3 \\ \Rightarrow \quad\left[\frac{x-x+8}{(x-8) \cdot x}\right]=\frac{3}{480} \\ \Rightarrow \quad \frac{8}{x^{2}-8 x}=\frac{1}{160} \\ \Rightarrow \quad x^{2}-8 x-1280=0 \\ \Rightarrow \quad x^{2}-40 x+32 x-1280=0 \\ \Rightarrow \quad x(x-40)+32(x-40)=0 \end{array} \\ \Rightarrow \\ (x-40)(x+32)=0 \\ \begin{array}{l} \Rightarrow \quad x-40=0 \text { or } x+32=0 \\ \Rightarrow \quad x=40 \text { or } x=-32 \end{array}$

But speed of the train cannot be -ve. Hence, the speed of the train =40 km/hr

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