Question

In a flight of 600 km , an aircraft was slowed down due to bad weather. The average speed for the trip was decreased by 200 km/h & the time of flight increased by 30 minutes. Find the duration of flight.

Answer 1

Actual duration with normal speed=1hrs
Duration with decreased speed=1.5hrs
1st method:
200 decrease==30mins or 1/2 hour more
200--1/2 hrs
400km in 1hr
600km in 1.5 hours (decreased speed)
600km/1.5hrs =400kmph is the decreased speed
Hence actual speed=400+200=600kmph
TIME=600km/600kmph= 1 HOUR
            2nd method
600km/X kmph = T hrs.....(1)
600km/X-200 kmph = T + 1/2 hrs...(2)
(2) - (1)
600/X-200 - 600/X = 1/2
[X-X+200]/X*(X-200) = 1/(2*600)
200/X*(X-200) = 1/1200
240000 = X*(X-200)
(either solve quadratically or trial and error by assuming,X=600,X-200=400)
240000= 600*400=240000
Hence actual speed,X=600kmph,D=600km, T=600/600=1hrs