Question

A car left $30$ minutes later than the scheduled time. In order to reach its destination $150$ km away in time, it has to increase its speed by $25$ km/hr from its usual speed. Find its usual speed.

Answer 1

Let $x$ be usual speed of the car in km/hr.

The increased speed of car$=(x+25)$ km/hr.

Distance$=150$km, Time $=\frac{Distance}{Speed}$

Let $T_1$,$T_2$ be the time taken by car to cover the given distance in usual time and decreased time.

Given $T_1-T_2=\frac{1}{2}$ $($ $\because$ ....$30$ minutes$=\frac{1}{2}$hour $)$

$\Rightarrow \frac{150}{x}-\frac{150}{x+25}=\frac{1}{2}$

$\Rightarrow \frac{1}{x}-\frac{1}{x+25}=\frac{1}{300}$

$\Rightarrow \frac{x+25-x}{x(x+25)}=\frac{1}{300}$

$\Rightarrow x(x+25)=7500$

$\Rightarrow x^2+25x-7500=0$

$\Rightarrow (x+100)(x-75)=0$

$\Rightarrow x=-100,75$

$\Rightarrow x=75$ ....$($ $\because$ $x=-100$ is not possible $)$

$\therefore$ the usual speed of the car is $75$ km/hr.