In a flight of 2800km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100km/h and time increased by 30 minutes. Find the original duration of the flight.

Explanation

Let the original speed of the aircraft be x km/hr.
Time taken to cover 2800 km `=(2800)/(x)` hours.
Reduced speed `=(x-100)km//hr.`
Time taken to cover 2800 km at this speed `=(2800)/((x-100))` hours.
`:." "(2800)/((x-100))-(2800)/(x)=(30)/(60)`
`implies" "(1)/((x-100))-(1)/(x)=(1)/(2xx2800)implies(x-(x-100))/((x-100)x)=(1)/(5600)`
`implies" "(100)/((x^(2)-100x))=(1)/(5600)impliesx^(2)-100x-560000=0`
`implies" "x^(2)-800x+700x-560000=0`
`implies" "x(x-800)+700(x-800)=0`
`implies" "(x-800)(x+700)=0`
`implies" "x-800=0" or "x+700=0`
`implies" " x=800" or "x=-700`
`implies" "x=800" "[because" speed cannot be negative"]`
`:." ""original speed of the aircraft"=800 km//hr.`
original duration of the flight `=(2800)/(800)` hours
= 3 hours 30 minutes.