Question

A passenger train takes one hour less for a journey of $150$ km if its speed is increased by $5$ km/hr from its usual speed. The usual speed of the train is----$km/hr$.

Answer 1

$\Rightarrow$ Let the usual speed of the train be $xkm/hr$

$\Rightarrow$ Distance covered in the journey$=150km$

$\Rightarrow$ Time taken by the train with usual speed $=\frac{150}{x}hr$

$\Rightarrow$ New speed of train $=(x+5)km/hr$

$\Rightarrow$ Time taken by the train after increasing the speed $=\frac{150}{x+5}hr$

$\frac{150}{x}-\frac{150}{x+1}=1$

$\Rightarrow$ $150(\frac{1}{x}-\frac{1}{x+5})=1$

$\Rightarrow$ $150\left(\frac{x+5-x}{x(x+5)}\right)=1$

$\Rightarrow$ $150\left(5\right)=x(x+5)$

$\Rightarrow$ $750=x^2+5x$

$\Rightarrow$ $x^2+5x-750=0$

$\Rightarrow$ $x^2+30x-25x-750=0$

$\Rightarrow$ $x(x+30)-25(x+30)=0$

$\Rightarrow$ $(x+30)(x-25)=0$

$\Rightarrow$ $x+30=0$ and $x-25=0$

$\Rightarrow$ $x=-30$ and $x=25$

Speed cannot be negative.

$\therefore$ The usual speed of the train is $25km/hr$