Question

A bus covers a distance of $24$ km at a uniform speed. Due to heavy rain its speed gets reduced by $10$ km/h and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be '$x$' km/h, from an equation and solve it to evaluate $x$.

Answer 1

The uniform speed $xkm/h$ and distance covered by it $24km$.

So, it takes $\frac{24}{x}h$ to cover the distance.

For heavy rain speed becomes $(x-10)km/h$

So, it will take time $=\frac{24}{(x-10)}h$

Hence we get $\frac{24}{x-10}-\frac{24}{x}=2$

$⟹x^2-10x-120=0$

$⟹x=\frac{10\pm \sqrt{100+480}}{2}=5\pm \sqrt{145}$

$⟹x\approx 17.04km/h$