In a flight of 2800km an aircraft was slowed down due to bar weather. If average speed is reduced by 100km/hr and time increase by 30min find the original duration of the 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 reduced by 30 min

New speed = (x – 100)
That is, 30 min = 30/60 hr = (1/2) hr

Time taken= 2800/(x – 100) hr
=2800/(x – 100)

= (2800/x) + (1/2)
2800/(x-100) - (2800/x) = 1/2

x² - 100x - 560000 = 0

x² - 800x + 700x - 560000 = 0

x(x - 800) + 700(x - 800) = 0
(x + 700) (x - 800) = 0
SO,

x = - 700 or 800

Thus original duration of the flight = 2800/800 = 7/2 hours
OR = 3 hr 30 mins

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