Answer :

Let the original speed of the plane be x km/h

Actual speed of the plane = (x + 100) km/h


Distance of journey = 1500km


Time taken to reach destination at original speed =


Time taken to reach destination at actual speed =


According to given question


30 mins = 1/2 hr






x2 + 100x = 300000


x2 + 100x – 300000 = 0


Using the splitting middle term – the middle term of the general equation is divided in two such values that:


Product = a.c


For the given equation a = 1 b = 100 c = – 300000


= 1. – 300000 = – 300000


And either of their sum or difference = b


= 100


Thus the two terms are 600 and – 500


Difference = 600 – 500 = 100


Product = 600. – 500 = – 300000


x2 + 600x – 500x + 300000 = 0


x (x + 600) – 500(x + 600) = 0


(x + 600)(x – 500) = 0


x = – 600 or x = 500


x = 500 (speed cannot be negative)


Hence the original speed of the plane is 500 km/hr


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