in a flight of 2800 km , aircraft was slowed down due to bad weather. its average speed is reduced by 100km/h and time increased by 30 mins. find original duration of flight.

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Solution

speed of aircraft= x
Distance = 2800 km

Time = Distance / Speed = 2800/x
Given:

The speed has reduced by 100 and time is increased by 30 min

time taken at normal speed = 2800/x hr

30 min = 30/60 hr = 1/2 hr

time taken after the speed was slowed down 2800/x - 100 hr

now, as per question,

time taken after the speed was slowed down =normal time taken +30min

2800/x-100 = 2800/x + 1/2hour

or 2800/x-100 - 2800/x = 1/2

or (2800x - 2800x + 280000) / x²-100x = 1/2

or 280000 / x²-100x = 1/2

or 560000 = x²-100x

or x²-100x-560000 = 0

or x²-800x+700x-560000 = 0

or x(x-800) + 700(x-800) = 0

or (x+700) (x-800) = 0

so x = 800

so original duration of the flight = 2800/800 hr

= 3 hr 30 min

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