Question

A bus covers a distance of $240km$ at a uniform speed. Due to heavy rain its speed gets reduced by $10km/h$ and as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be $xkm/h$, form an equation and solve it to evaluate the value of $x$ (in $km/hr$)

Answer 1

Uniform speed $=xkm/h$

distance $=240km$

time $=\frac{\text{Distance}}{\text{Speed}}$

$=\frac{240}{x}hours$

Due to heavy rain speed $=(x-10)km/h$

Now time $=\frac{240}{x-10}$ hours

According to question

$\frac{240}{x-10}-\frac{240}{x}=2$

$\frac{240x-240(x-10)}{x(x-10)}=2$

$\frac{240x-240x+2400}{x^2-10x}=2$

$\Rightarrow 2x^2-20x-2400=0$

$\Rightarrow x^2-10x-1200=0$

$x^2-40x+30x-1200=0$

$x(x-40)+30(x-40)=0$

$\Rightarrow (x-40)(x+30)=0$

$x=40$ and $x=-30$ (speed can not be negative)

$\therefore$ uniform speed $=40km/h$.