# While boarding an

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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