Question

In a flight of 2800km an aircraft was slowed down due to bad wheather its average speed is reduce by 100km/h

Answer 1

$\huge{\underline{\bf{\purple{Question:-}}}}$

In a flight of 2800km an aircraft was slowed down due to bad wheather its average speed is reduce by 100km/hr and time of flight increased by 30min .find the original duration of the flight.

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$\large{\underline{\bf{\pink{Answer:-}}}}$

✰ The original duration of the flight = 3 h and 30min

$\large{\underline{\bf{\blue{Explanation:-}}}}$

$\large{\underline{\bf{\green{Given:-}}}}$

✰ Total distance = 2800km

✰ average speed reduced = 100km/hr

✰ Time increased by flight = 30minutes

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the original duration of the flight.

$\huge{\underline{\bf{\red{Solution:-}}}}$

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

Time taken to cover 2800km=$\frac{2800}{x}hours.$

Reduced speed =(x -100 )km/hr.

Time taken to cover 2800km at this speed =$\frac{2800}{(x-100)}hours.$

Therefore $\frac{2800}{(x-100)}-\frac{2800}{x}=\frac{30}{60}$

$:\implies \: \frac{1}{(x - 100)} - \frac{1}{x} = \frac{1}{2 \times 2800} \\ \\ :\implies \: \frac{x - (x - 100)}{(x - 100)x} = \frac{1}{5600} \\ \\:\implies \: \frac{100}{ {x}^{2} - 100x } = \frac{1}{5600} \\ \\ :\implies \: {x}^{2} - 100x - 560000 = 0$

$:\implies \:$ x² - 800x + 700x -560000 = 0

$:\implies \:$x(x -800) +700(x - 800)

$:\implies \:$(x -800)(x +700)

$:\implies \:$x -800 = 0 or x+ 700 = 0

$:\implies \:$x = 800 or x = -700

$:\implies \:$ x = 800

[ speed can not be negative].

So ,the original speed of the aircraft = 800km/hr.

original duration of the flight = 2800/800hours

⠀⠀⠀⠀$:\implies \:$= 3 hours 30 minutes.

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