# While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?

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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