Name: Nature of the Roots: Illustration
Uploaded: 2019-07-19
Duration: 2 min 4 s
Description: We cannot judge a book by its cover, but we can find the nature of the roots of a given quadratic equation without finding roots. Let's learn just how we can...

Question

A train covers a distance of

480 km

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. Find the usual speed of the train.

Accepted Answer

Consider, the usual speed of the train be $x km / h$ and Reduced speed of the train $= (x - 8) km / h$

Total distance to be covered $= 480 km$

Time taken by the train to cover the distance at usual speed $= \frac{480}{x} h$

Time taken by the train to cover the distance at reduced speed $= \frac{480}{x - 8} h$

According to the given condition,

Time taken by the train to cover the distance at reduced speed $=$ Time taken by the train to cover the distance at usual speed $+ 3 h$

$∴ \frac{480}{x - 8} = \frac{480}{x} + 3$

$\Rightarrow \frac{480}{x - 8} - \frac{480}{x} = 3$

$\Rightarrow \frac{480 x - 480 x + 3840}{x (x - 8)} = 3$

$\Rightarrow \frac{3840}{x^{2} - 8 x} = 3$

$\Rightarrow \frac{1280}{x^{2} - 8 x} = 1$

$\Rightarrow x^{2} - 8 x = 1280$

$\Rightarrow x^{2} - 8 x - 1280 = 0$

$\Rightarrow x^{2} - 40 x + 32 x - 1280 = 0$

$\Rightarrow x (x - 40) + 32 (x - 40) = 0$

$\Rightarrow (x - 40) (x + 32) = 0$

$\Rightarrow x - 40 = 0$ or $x + 32 = 0$

$\Rightarrow x = 40$ or $x = - 32$

$x = 40$ (Speed cannot be negative)

Therefore, the usual speed of the train is $40 km / h$ .

A train covers a distance of $480 km$ 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. Find the usual speed of the train.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

A train covers a distance of 480 km 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. Find the usual speed of the train.

Important Questions on Quadratic Equations

Learn and Prepare for any exam you want !

A train covers a distance of $480 km$ 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. Find the usual speed of the train.