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

let speed be x km/hr

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,

  2800/x-100  =  2800/x + 1/2

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    Ans.