Question

In a flight of 600 km, the speed of the aircraft was slowed down due to bad weather. The average speed of the trip was decreased by 200 km/hr and thus the time of flight increased by 30 minutes. Find the average speed of the aircraft originally.

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Answer 1

Let us consider the original speed of the flight to be x km/hr

Then, the new speed of the flight = (x - 200) km/hr

Now,

Flight time at original speed =  $\frac{600}{x} hr$

and, flight time at new speed = $\frac{600}{x-200} hr$

∵ the change in speed increased the flight time by 30 minutes;

i.e.,

(flight time at new speed) - (flight time at original speed) = $\frac{1}{2} hr$

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

⇒ $\frac{600x - 600(x-200)}{x(x-200)}$ = $\frac{1}{2}$

⇒ $\frac{120000}{x^2 - 200x}$ = $\frac{1}{2}$

⇒ $x^2 - 200x - 240000 = 0$

⇒ $x^2 - 600x + 400x - 240000$ = 0 (middle term factor)

⇒ $(x-600) (x+400) = 0$

⇒ $x = 600$ or $x = (-400)$

∵ speed cannot be a negative figure

∴ the original speed of the aircraft was 600 km/hr

Ans) The original speed of the aircraft = 600 km/hr