Question

in a flight of 6000 km an aircraft was slowed down due to bad weather its average speed for the trip was reduced by 400 km per hour and time increase by 30 minutes find original duration of flight

Answer 1

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

Decreased speed of the aircraft = (x - 400) km/hr

Time = Distance/Speed

Original duration of the flight = (6000 / x) hrs

Duration of the flight with decreased speed = (6000 / x-400) hrs

Difference of time = 30 min = 1/2 hrs

⇒ (6000 / x-400) - (6000 / x) = 1/2

⇒ (6000x - 6000x + 2400000) / x(x - 400) = 1/2

⇒ x2 - 400x = 4800000

⇒ x2 - 400x - 4800000 = 0

⇒ (x - 2400)(x + 2000) = 0

⇒ x = 2400 or -2000

Positive value of x is 2400.

Therefore original speed of the aircraft is 2400 km/hr.

Original duration of the aircraft = 6000/2400 = 2.5 hrs.