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In a flight of 6000 km, an aircraft was ...

In a flight of 6000 km, an aircraft was slowed down due to bad weather. The average speed for the trip was reduced by 400 km/h and the time of flight increased by 30 min. Find the original duration of the flight.

Text Solution

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original duration=t hr
Increased duration=(t+1/2)hr
Initial speed=6000/t km/h
reduced speed=6000/(t+1/2) km/h
`6000/t-6000/(t+1/2)=400`
`(6000t+3000-6000t)/(t(t+1/2))=400`
`2t^2+t-15=0`
`t=(-1pmsqrt(1+120))/4=5/2hr`
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