# The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train.

Question:

The distance between Mumbai and Pune is 192 km. Travelling by the Deccan Queen, it takes 48 minutes less than another train. Calculate the speed of the Deccan Queen if the speed of the two trains differ by 20 km/hr.

Solution:

Let the speed of the Deccan Queen be $x \mathrm{~km} / \mathrm{hr}$.

According to the question:

Speed of another train $=(\mathrm{x}-20) \mathrm{km} / \mathrm{h}$

$\therefore \frac{192}{x-20}-\frac{192}{x}=\frac{48}{60}$

$\Rightarrow \frac{4}{x-20}-\frac{4}{x}=\frac{1}{60}$

$\Rightarrow \frac{4 x-4(x-20)}{(x-20) x}=\frac{1}{60}$

$\Rightarrow \frac{4 x-4 x+80}{x^{2}-20 x}=\frac{1}{60}$

$\Rightarrow \frac{80}{x^{2}-20 x}=\frac{1}{60}$

$\Rightarrow x^{2}-20 x=4800$

$\Rightarrow x^{2}-20 x-4800=0$

$\Rightarrow x^{2}-(80-60) x-4800=0$

$\Rightarrow x^{2}-80 x+60 x-4800=0$

$\Rightarrow x(x-80)+60(x-80)=0$

$\Rightarrow(x-80)(x+60)=0$

$\Rightarrow x=80$ or $x=-60$

The value of $x$ cannot be negative; therefore, the original speed of Deccan Queen is $80 \mathrm{~km} / \mathrm{hr}$.