Question

Represent the given situation in the form of a quadratic equation: 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.

Answer 1

Given: A train travels a distance of $480km$ 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.

To find: quadratic equation of the situation

Sol: Distance travelled by the train = $480km$

Let the speed of the train be $x$ kmph

Time taken for the journey = $\frac{480}{x}$

Given speed is decreased by $8kmph$

Hence the new speed of train = $(x–8)kmph$

Time taken for the journey =$\frac{480}{(x–8)}$

$⟹\frac{480}{x-8}-\frac{480}{\left(x\right)}=3⟹480(x-x+8)=3x(x-8)⟹x^2-8x=\frac{480\times 8}{3}⟹x^2-8x=1280⟹x^2-8x-1280=0$

represents the given situation in a quadratic equation.