Question

A passenger train takes $2$ hours less for a journey of $300$ km if its speed is increased by $5km/hr$ from its usual speed. Find its usual speed of the train.

Answer 1

Let the usual speed of the train is $xkm/h$.

$D=300km$ (Given)

$Speed=\frac{Distance}{Time}$

$Time=\frac{300}{x}$

After increasing the speed of the train ;

New speed is $(x+5)km/h$

$Time=\frac{300}{x+5}$

Now, difference between the time taken by usual speed and after increasing speed of the train is two hours. Therefore,

$\frac{300}{x}-\frac{300}{x+5}=2$

$\Rightarrow 300(\frac{1}{x}-\frac{1}{x+5})=2$

$\Rightarrow \left(\frac{x+5-x}{x^2+5x}\right)=\frac{2}{300}$

$\Rightarrow \frac{5}{x^2+5x}=\frac{1}{150}$

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

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

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

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

$\Rightarrow x=25,-30$

Ignore the negative value of the speed.

Hence, the usual speed of the train is $25km/hr$.