Question:
In a flight of 2800km , an air craft 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
Answer:
Let the average speed of the aircraft = x km/hr
Now, new speed = (x - 100) km/hr
total distance to be covered = 2800 km
Now, duration of flight with average speed t1 = 2800/x hr
and duration of flight with new speed t2 = 2800/(x - 100) hr
Now, according to question,
t2 - t2 = 30 minutes
=> t2 - t2 = 1/2 hr
=> 2800/(x -100) - 2800/x = 1/2
=> 2800{1/(x -100) - 1/x} = 1/2
=> 2800[{x - (x - 100)}/{x*(x -100)}] = 1/2
=> 2800[{x - x + 100}/{x*(x -100)}] = 1/2
=> 2800[100/{x*(x -100)} = 1/2
=> 2800*100*2 = x*(x -100)
=> 560000 = x2 - 100x
=> x2 - 100x - 560000 = 0
=> (x - 800)*(x + 700) = 0
=> x = 800, -700
Since speed can not be negative,
So, x = 800
=> speed of the aircraft = 800
Original duration = 2800/x = 2800/800 hr = 3 hr 30 minutes
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