A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

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(x^{2} + 20x)

350x + 3000 = 5x^{2} + 100x

5x^{2} – 250x – 3000 = 0

x^{2} – 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

x^{2} – 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

43