A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h$ less, then it would have taken $3$ hours more to cover the same distance. Find the actual speed of the train.

Open in App

Solution

Distance travelled by the train = $480 k m$
Let the speed of the train be $x k m p h$
Time taken for the journey = $\frac{480}{x}$
Given speed is decreased by $8 k m p h$
Hence the new speed of train = $(x - 8) k m p h$
Time taken for the journey = $\frac{480}{x - 8}$
$\Rightarrow$ $\frac{480}{x - 8} - \frac{480}{x} = 3$
$\Rightarrow$ $\frac{480 (x - x + 8)}{x (x - 8)} = 3$
$\Rightarrow$ $\frac{480}{3} \times 8 = x^{2} - 8 x$

$\Rightarrow$ $1280 = x^{2} - 8 x$
$\Rightarrow x^{2} - 8 x - 1280 = 0$
$\Rightarrow x^{2} - 40 x + 32 x - 1280 = 0$
$\Rightarrow x (x - 40) + 32 (x - 40) = 0$
$\Rightarrow (x + 32) (x - 40) = 0$

Either $x + 32 = 0$ or $x - 40 = 0$

As, speed cannot be in negative values, hence , we get $x = 40$ .

Thus, the speed of the train is $40 k m p h$ .

Suggest Corrections

Similar questions

A train covers a distance of 480 km at a uniform speed. If speed had been 8km /hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h r$ less, then it would have taken $3$ hours more to cover the same distance. The speed of the train is ___ kmph.

A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h r$ less, then it would have taken $3$ hours more to cover the same distance. The original speed of the train is ___ km/hr.