Q42 of 186 Page 4

A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it has to increase the speed by 250 km/hr from the usual speed. Find its usual speed.

Let the usual time taken by the aeroplane = x km/hr

Distance to the destination = 1500km


We know that,



Hence, speed


According to the question,


Plane left 30min later than the scheduled time


30min


Time taken by the aeroplane


∴ the speed of the plane


Given that speed has to increase by 250 km/hr






⇒ 6(2x – 2x + 1) = 2x2 – x


⇒ 6 = 2x2 – x


⇒ 2x2 –x – 6 = 0


⇒ 2x2 – 4x + 3x – 6 = 0


⇒ 2x (x – 2) + 3 (x – 2) = 0


⇒ (2x + 3) (x – 2) = 0


⇒ (2x + 3) = 0 or (x – 2) = 0


∴ or x = 2


Since, time can’t be negative.


Hence, the time taken by the aeroplane is 2hrs and the speed is 750km/hr


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