Question

in a flight of 600km, a aircraft was slowed down due to bad weather.Its average speed for the trip was reduced by 200km/hr and the time of the flight increased by 30min. Find the duration of flight

Answer 1

let the average speed of the aircraft = u km/h

speed=distance/time

time=distance/speed

time=distance/u

600/u-200=600/u+1/2  (30min=1/2h)

600/u-200=1200+u/2u

by cross multiplication

1200u=1200u+u2-240000-200u

0=u2-200u-240000

0=u2-600u+400u-240000

u(u-600)+400(u-600)

(u+400)(u-600)

therefore u=600 or -400

since speed cant be in negative u=600km/h

time=distance/speed

=600/600

=1hour

so the duration of the flight in average speed is 1hour

but when the speed was reduced the duration was increased by 30min

therefore the speed of flight when reduced the duration will be 1hour 30min

Answer 2

x=600 or ,x=-400→x=600
so the origional speed of the aircraft was 600 km/hr.
hence , duration if flight =[600/x]hr=[600/600]hr=1hr