Question

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200km. Find the speed of the aeroplane.

• A. 1, 3
• B. –1, 3
• C. –1, –3
• D. 1, –1

Answer 1

The correct option is A

1, 3

Let the speed of the aeroplane be $x$ km/hr
Time = $\frac{Distance}{Speed}$
$\therefore$ Time taken to cover 1200km = $\frac{1200}{x}$
Reduced speed = $x-40$ km/hr
$\therefore$ Time taken to cover 1200km in reduced speed = $\frac{1200}{x-40}$
Given:
$\frac{1200}{x-40}$ - $\frac{1200}{x}=\frac{1}{3}$ [ 20 minutes = $\frac{1}{3}$ hours]
$\Rightarrow$ $\frac{48000}{x(x-40)}=\frac{1}{3}$
$\Rightarrow$ $144000=x^2-40x$
$\Rightarrow$ $x^2-40x-144000=0$
$\Rightarrow$ $x^2-400x+360x-144000=0$
$\Rightarrow$ $x(x-400)+360(x-400)=0$
$\Rightarrow$ $(x+360)(x-400)=0$
$\Rightarrow$ $x=-360orx=400$
Since speed cannot be negative, we get x = 400 km/hr