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Hint: The main formula in this question that would be used is as follows

\[distance=speed\times time\]

Another important thing that is used in the question is that due to bad weather the speed of the aircraft would be reduced and the flight time would be increased.

Complete step-by-step answer:

As mentioned in the question, we have to calculate the duration of the flight.

Now, using the formula which is mentioned in the hint, we can form the equation as follows

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

When due to bad weather, the new speed can be written as (x−200) km/hr

Now, the duration of the flight at original speed can be written as follows

\[=\left( \dfrac{600}{x} \right)\ hr\]

Now, the duration of fight at the reduced speed can be written as

\[=\left( \dfrac{600}{x-200} \right)\ hr\]

Now, as the flight time of the aircraft is increased by 30 minutes, we can write the equation as follows

\[\begin{align}

& \left( \dfrac{600}{x-200} \right)\ -\left( \dfrac{600}{x} \right)\ =\dfrac{1}{2} \\

& \dfrac{600x-600\left( x-200 \right)}{{{x}^{2}}-200x}=\dfrac{1}{2} \\

& 1200x-1200x+240000={{x}^{2}}-200x \\

& {{x}^{2}}-200x-240000=0 \\

& \left( x-600 \right)\left( x+400 \right)=0 \\

\end{align}\]

Hence, the actual speed of the aircraft is 600km/hr. Therefore, the actual time of the flight or the duration of the flight is \[\left( \dfrac{600}{600} \right)=1\ hr\] .

Note: The students can make an error will evaluating the actual time of the flight if the students don’t know the relation between distance, speed and time which is given in the formula in the hint that is

\[distance=speed\times time\].

\[distance=speed\times time\]

Another important thing that is used in the question is that due to bad weather the speed of the aircraft would be reduced and the flight time would be increased.

Complete step-by-step answer:

As mentioned in the question, we have to calculate the duration of the flight.

Now, using the formula which is mentioned in the hint, we can form the equation as follows

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

When due to bad weather, the new speed can be written as (x−200) km/hr

Now, the duration of the flight at original speed can be written as follows

\[=\left( \dfrac{600}{x} \right)\ hr\]

Now, the duration of fight at the reduced speed can be written as

\[=\left( \dfrac{600}{x-200} \right)\ hr\]

Now, as the flight time of the aircraft is increased by 30 minutes, we can write the equation as follows

\[\begin{align}

& \left( \dfrac{600}{x-200} \right)\ -\left( \dfrac{600}{x} \right)\ =\dfrac{1}{2} \\

& \dfrac{600x-600\left( x-200 \right)}{{{x}^{2}}-200x}=\dfrac{1}{2} \\

& 1200x-1200x+240000={{x}^{2}}-200x \\

& {{x}^{2}}-200x-240000=0 \\

& \left( x-600 \right)\left( x+400 \right)=0 \\

\end{align}\]

Hence, the actual speed of the aircraft is 600km/hr. Therefore, the actual time of the flight or the duration of the flight is \[\left( \dfrac{600}{600} \right)=1\ hr\] .

Note: The students can make an error will evaluating the actual time of the flight if the students don’t know the relation between distance, speed and time which is given in the formula in the hint that is

\[distance=speed\times time\].

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