Question

A car covers a distance of $240$ km with some speed. If the speed is increased by $20$ km/hr, it will cover the same distance in $2$ hours less. Find the speed of the car.

• A. $40$
• B. $45$
• C. $50$
• D. $60$

Answer 1

The correct option is A $40$

Let the speed of the car be $s$ and time be $t$

Then, $st=240⟹s=\frac{240}{t}$

and $(s+20)(t-2)=240$

$(\frac{240}{t}+20)(t-2)=240$

$(20t+240)(t-2)=240t$

$20t^2+240t-480-40t=240t$

$20t^2-40t-480=0$

$t^2-2t-24=0$

$t^2-6t+4t-24=0$

$(t-6)(t+4)=0$

$t=-4,6$

Hence, time is $6$ hr

and speed $=\frac{240}{6}=40km/hr$