# A truck covers a

Let the first speed of the truck be x km/h

Time taken to cover 150 km =

New speed of truck = x + 20 km/h

Time taken to cover 200 km =

According to given question

350x + 3000 = 5(x2 + 20x)

350x + 3000 = 5x2 + 100x

5x2 – 250x – 3000 = 0

x2 – 50x – 600 = 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 = – 50 c = – 600

= 1. – 600 = – 600

And either of their sum or difference = b

= – 50

Thus the two terms are – 60 and 10

Difference = – 60 + 10 = – 50

Product = – 60.10 = – 600

x2 – 60x + 10x – 600 = 0

x (x – 60) + 10(x – 60) = 0

(x – 60) (x + 10) = 0

x = 60 or x = – 10

x = 60 (speed cannot be negative)

Hence the first speed of the truck is 60 km/hr

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