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In a flight of 600 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 30 minutes. The duration of the flight is:

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Detailed Solution

Let the duration of the flight be x hours.

Then,

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

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

$\Rightarrow x = 1 hr$ [neglecting the -ve value of $x$ ] .

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