Question

In a flight 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. The duration of the flight is:

• A. $1$ Hour
• B. $3$ Hours
• C. $2$ Hours
• D. $4$ Hours

Answer 1

Answer: (A)

$1$ Hour

Let the duration of the flight be $x$ hours.

It is given that the average speed for the trip was reduced by $200$ km/hr and the time of flight increased by $30$ minutes, therefore, we have:

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

$\Rightarrow \frac{600}{x}-\frac{1200}{2x+1}=200$

$\Rightarrow \frac{600(2x+1)}{x(2x+1)}-\frac{1200x}{x(2x+1)}=200$

$\Rightarrow \frac{1200x+600-1200x}{x(2x+1)}=200$

$\Rightarrow \frac{600}{x(2x+1)}=200$

$\Rightarrow x(2x+1)=\frac{600}{200}$

$\Rightarrow x(2x+1)=3$

$\Rightarrow {2x}^2+x=3$

$\Rightarrow {2x}^2+x-3=0$

$\Rightarrow {2x}^2-2x+3x-3=0$

$\Rightarrow 2x(x-1)+3(x-1)=0$

$\Rightarrow (2x+3)(x-1)=0$

$\Rightarrow (2x+3)=0,(x-1)=0$

$\Rightarrow x=-\frac{3}{2},x=1$

Ignoring the negative values, we have $x=1$.

Hence, the duration of the flight is $1$ hour.