A bus covers a distance of 240 km at an uniform speed. Due to heavy rain, its speed gets reduced by 10 kmph and as such it takes two hours longer to cover the distance. Assuming the uniform speed to be x kmph, form an equation and solve it to evaluate x.
Original speed of bus $=x \ kmph$
Distance $=240 \ km$
Time taken to cover 240 km $= \dfrac{240}{x} \ hours$
New speed of bus $=\left(x-10\right) \ kmph$
$\therefore$ New time taken to cover 240 km $= \dfrac{240}{x-10} \ hours$
$\therefore$ As per sum,
$\dfrac{240}{x-10}=\dfrac{240}{x}+2$
i.e. $120x = 120x -1200 + x \left(x-10\right)$
i.e. $x^2 - 10x - 1200 = 0$
i.e. $x^2 - 40x + 30 x -1200=0$
i.e. $x \left(x-40\right) + 30 \left(x-40\right)=0$
i.e. $\left(x-40\right)\left(x+30\right)=0$
i.e. $x=40$ or $x=-30$
Since the speed of the bus cannot be negative
$\therefore$ original speed of the bus $= 40 \ kmph$