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

By formula,

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Distance to be covered by bus = 240 km

Time taken by bus at original speed = $\dfrac{240}{x}$

Time taken by bus at reduced speed = $\dfrac{240}{x - 10}$

Given,

On decreasing the speed, it takes two hours longer to cover distance.

$\Rightarrow \dfrac{240}{x - 10} - \dfrac{240}{x} = 2 \\[1em] \Rightarrow \dfrac{240x - 240(x - 10)}{x(x - 10)} = 2 \\[1em] \Rightarrow \dfrac{240x - 240x + 2400}{x^2 - 10x} = 2 \\[1em] \Rightarrow 2400 = 2(x^2 - 10x) \\[1em] \Rightarrow \dfrac{2400}{2} = (x^2 - 10x) \\[1em] \Rightarrow 1200 = x^2 - 10x \\[1em] \Rightarrow 0 = x^2 - 10x - 1200 \\[1em] \Rightarrow x^2 - 10x - 1200 = 0 \\[1em] \Rightarrow x^2 - 40x + 30x - 1200 = 0 \\[1em] \Rightarrow x(x - 40) + 30(x - 40) = 0 \\[1em] \Rightarrow (x + 30)(x - 40) = 0 \\[1em] \Rightarrow (x + 30) = 0 \text{ or } (x - 40) = 0 \text{….[Using zero-product rule]} \\[1em] \Rightarrow x = -30 \text{ or } x = 40.$

x = 40 [speed must be positive]

Hence, the equation formed is x² - 10x - 1200 = 0 and the speed of bus = 40 km/hr.