Question

In a flight of $400$ km, 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 $1$ hour. The duration of the flight is

• A. $1$ hour
• B. $2$ hours
• C. $3$ hours
• D. $4$ hours

Answer 1

The correct option is A $1$ hour

Let the duration of the flight be $x$ hours.
Then, $\frac{400}{x}-\frac{400}{x+1}=200$
$400x+400-400x=200$ $(x^2+x)$
$400=$ $200x^2+200x$
$200x^2+200x-400$
Divide $200$ on both the sides, we get,
$x^2+x-2=0$
$(x+2)(x-1)=0$
$x=1$ hour (neglecting the negative value of $x$)