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In a flight of $600$ km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by $200$ km/h from its usual speed and time of flight increased by $30$ minutes. Find the scheduled duration of the flight.
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Sol. Let the average speed of the aircraft be $x$ km/h
Time taken by aircraft $= \frac{600}{x}$
Time taken by aircraft when flight is delayed by $30$ min $= \frac{600}{x-200}$
frac{600}{x-200} -
frac{600}{x} =
frac{1}{2}$$\begin{aligned}& (2 Marks) \\ & x^2-200x - 240000 = 0\end{aligned}$$ (1 Mark)
Rightarrow (x-600)(x + 400) = 0$$\begin{aligned}& (1 Mark) \\ & x = 600, x = - 400 \\ & x = - 400\end{aligned}$$ (rejected) (1/2 Mark)
therefore x = 600$\\therefore$ Scheduled duration of the flight $= \frac{600}{600} = 1$ hour (1/2 Mark)
Time taken by aircraft $= \frac{600}{x}$
Time taken by aircraft when flight is delayed by $30$ min $= \frac{600}{x-200}$
frac{600}{x-200} -
frac{600}{x} =
frac{1}{2}$$\begin{aligned}& (2 Marks) \\ & x^2-200x - 240000 = 0\end{aligned}$$ (1 Mark)
Rightarrow (x-600)(x + 400) = 0$$\begin{aligned}& (1 Mark) \\ & x = 600, x = - 400 \\ & x = - 400\end{aligned}$$ (rejected) (1/2 Mark)
therefore x = 600$\\therefore$ Scheduled duration of the flight $= \frac{600}{600} = 1$ hour (1/2 Mark)