##### A train covers a distance of 480 km at a uniform speed. If the speed had been 8 km/hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

Let the usual speed of the train be x km/h

Reduced speed of the train = (x – 8) km/h

Distance of journey = 480km

Time taken to reach destination at usual speed = Time taken to reach destination at reduced speed = According to given question    x2 – 8x = 1280

x2 – 8x – 1280 = 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 = – 8 c = – 1280

= 1. – 1280 = – 1280

And either of their sum or difference = b

= – 8

Thus the two terms are – 40 and 32

Difference = – 40 + 32 = – 8

Product = – 40.32 = – 1280

x2 – 40x + 32x – 1280 = 0

x (x – 40) + 32(x – 40) = 0

(x – 40)(x + 32) = 0

x = 40 or x = – 32

x = 40 (speed cannot be negative)

Hence the usual speed of the train is 40 km/h

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