Answer :

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


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses