Question

In a fight of $600km$, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by $200$ km/hr and the time of flight increased by $30$ minutes. Find the duration of flight.

Answer 1

Let the original speed of the aircraft be $x$ km/hr.

then new speed $=(x-200)$ km.hr

Duration of flight at original speed $=\left(\frac{600}{x}\right)hr$

Duration of fight at reduced speed $=\left(\frac{600}{x-200}\right)hr$

$\therefore \frac{600}{x-200}-\frac{600}{x}=\frac{1}{2}$

$\Rightarrow \frac{600x-600(x-20)}{x(x-200)}=\frac{1}{2}\Rightarrow \frac{120000}{x^2-200x}=\frac{1}{2}$

$\Rightarrow x^2-200x-240000=0\Rightarrow x^2-600x+400x-240000=0$

$\Rightarrow (x-600)(x+400)=0\Rightarrow x=600orx=-400\Rightarrow x=600$

So, the origianl speed of the aircraft was $600km/hr$

hence, duration of flight $=\left(\frac{600}{x}\right)hr=\left(\frac{600}{60}\right)hr=1hr$