Question

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

Answer 1

Let the original speed be x km/hr.

Time taken by the bus with moving at speed x km/h = $\frac{240}{x}$

Time taken by the bus with moving at a speed (x-10) km/h = $\frac{240}{x-10}$

According to the given condition,

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

$\Rightarrow$ $2=240(\frac{1}{x-10}-\frac{1}{x})$

$\Rightarrow$ $\frac{1}{120}=\frac{1}{x-10}-\frac{1}{x}$

$\Rightarrow$ $\frac{1}{120}=\frac{x-x+10}{x(x-10)}$

$\Rightarrow$ $x(x-10)=10\times 120$

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

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

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

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

$\Rightarrow$ $x-40=0orx+30=0$

$\Rightarrow$ x = 40 or x = -30

Since, the speed cannot be negative, the uniform speed is 40 kmph.