Question

A bike travels a distance of $200km$ at a constant speed. If the speed of the bike is increased by $5km/hr$ the journey would have taken $2$ hours less. What is the speed of the bike?

• A. $30km/hr$
• B. $25km/hr$
• C. $20km/hr$
• D. $15km/hr$

Answer 1

Answer: (C)

$20km/hr$

Let the constant speed of the bike be $xkm/hr$.

Then $\frac{200}{x}-\frac{200}{(x+5)}=2$
$\Rightarrow \frac{200(x+5)-200x}{x(x+5)}=2$

$\Rightarrow \frac{1000}{x^2+5x}=2$
$\Rightarrow x^2+5x-500=0$

$\Rightarrow x^2+25x-20x-500=0$
$\Rightarrow x(x+25)-20(x+25)=0$

$\Rightarrow (x+25)(x-20)=0$
$\Rightarrow x=-25$ or $20$

$\Rightarrow x=20km/hr$ ($\because$ speed is not negative)