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 as such it takes two hrs longer to cover the total distance. Assuming the uniform speed to be `x` km/h form an equation and solve it to evaluate `x`.

Answer 1

Then let the speed of the bus be$\frac{xkm}{hr}$
Then time taken by the bus for the first=$\frac{240}{x}$ hrs.
and
time taken by the bus after raining to cover the remaining distance =$\frac{240}{x-10}$

by the question we have,

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

$\frac{(240x-24)-(x-10)}{(x-10)\left(x\right)}=2$

$\to 240x-240x+2400=2x(x-10)$
$\to 2400=2x(x-10)$
$\to 2x^2-20x-2400=0$
$\to x^2-10x-1200=0$
$\to x^2-(40-30)x-1200=0$
$\to x(x-40)+30(x-40)=0$
$\to =40\frac{km}{hr}$

Hence the speed of the bus=$40\frac{km}{hr}$