flight of 6000 km an aircraft was slowed down due to bad weather its average speed was the trip was reduced by 400 km per hour and time increase by 30 minutes find the original duration of the flight
flight of 6000 km an aircraft was slowed down due to bad weather its average speed was the trip was reduced by 400 km per hour and time increase by 30 minutes find the original duration of the flight
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Answer:
Step-by-step explanation:
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. Or 2½ hr