Class 10

Math

All topics

Complex Number and Quadratic Equations

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/hr$ less, then it would have taken $3$ hours more to cover the same distance. Formulate the quadratic equation in terms of the speed of the train.

Time taken to travel a distance of $480km=x480 hr$

Time taken by the train to travel a distance of $480km$ with the speed $(x−8)km/hr=x−8480 hr$

It is given that if the speed had been $8km/hr$ less, then the train would have taken $3$ hours more to cover the same distance

$∴x−8480 =x480 +3$

$⇒x−8480 −x480 =3⇒x(x−8)480(x−x+8) =3⇒x(x−8)480×8 =3$

$⇒3x(x−8)=480×8⇒x(x−8)=160×8⇒x_{2}−8x−1280=0$

This is the required quadratic equation.