Question

A man drives his car on the highway where the speed limit is $60$ kmph. He has to cover a distance of $240$ km at a uniform speed on the road. If he increases his speed by $20$ kmph, he can reach the destination 1 hour earlier. What is his original speed?

• A. $20$ kmph
• B. $5$ kmph
• C. $60$ kmph
• D. $30$ kmph

Answer 1

The correct option is C $60$ kmph

Speed limit on the highway is $60$ kmph.

Distance to cover, $d=240$ km

Let first time, the speed is $s$ kmph and the time to cover the distance is $t$ hours.

then, $s=\frac{d}{t}$

$s=\frac{240}{t}$

$t=\frac{240}{s}$ ...........(1)

Now, if the speed is increased by $20$ kmph, time taken is $t-1$ hours.

then, $s+20=\frac{d}{t-1}$

$s+20=\frac{240}{t-1}$

$t-1=\frac{240}{s+20}$

$t=\frac{240}{s+20}+1$ .........(2)

From (1) and (2),

$\frac{240}{s}$$=\frac{240}{s+20}+1$

$\frac{240}{s}-1$$=\frac{240}{s+20}$

$\frac{240-s}{s}$$=\frac{240}{s+20}$

$s^2+20s-4800=0$

$(s+80)(s-60)=0$

$s=-80$ or $s=60$

Speed cannot be negative, so original speed is $60$ kmph.