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A plane left 30 min later than the scheduled time and in order to reach the destination 1500km away in time it has to increase the speed by 250km/h from

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Given ;-

⇒ Time taken by the plane after the scheduled time = 30 min

⇒ Total distance = 1500 km

⇒Increased. speed of aeroplane from the usual speed = 250 km / hr

To find :-

⇒Usual speed of aeroplane = ?

Sol ;-

⇒We dont know the usual speed so let us take usual speed as x.

Usual speed = x

⇒Total distance travelled by aeroplane = 1500 km

Speed of aeroplane -

⇒Speed = Distance / Time = (1500 / x) Hrs { As we dont know time taken so let us take it as x }

⇒ {case - 1 }

⇒Total .Time taken by the aeroplane to travel = ( x - 1/2 ) Hrs

⇒ Distance travelled by aeroplane = 1500 km Therefore we get the speed as ,

⇒Speed = Distance / Time

= 1500 / (x - 1/2) Hrs [ Case - 2 ]

Total. increased speed by the aeroplane is 250 km / hr .

⇒ Case - 1 - Case - 2 = Increased speed

⇒ [ 1500 / ( x - 1 /2 ] - [ 1500 / x ] = 250

⇒ 1 / ( 2 x² - x ) = 1/6

⇒ 2x² - x = 6

⇒ ( x - 2 ) ( 2 x + 3 ) = 0

Therefore we get x as

⇒ x = 2

⇒ So, the usual time taken by aeroplane = 2 hrs

Usual speed = Total distance / Usual time taken = 1500 / 2