Question

Question 2(iv)
Represent the following situations in the form of quadratic equations.
(iv) A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train.

Answer 1

(iv) Distance travelled by train = $480km$
Let the speed of the train be $xkmph$.
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 = $\frac{480}{x-8}$
$\Rightarrow$ $\frac{480}{x-8}-\frac{480}{x}=3$
$\Rightarrow$ $\frac{480(x-x+8)}{x(x-8)}=3$
$\Rightarrow$ $\frac{480}{3}\times 8=x^2–8x$

$\Rightarrow$ $1280=x^2–8x$
$\Rightarrow x^2-8x-1280=0$
$\Rightarrow x^2-40x+32x-1280=0$
$\Rightarrow x(x-40)+32(x-40)=0$
$\Rightarrow (x+32)(x-40)=0$
Either $x+32=0orx-40=0$
As, speed cannot be a negative value,
We get, $x=40$
Thus, the speed of the train is $40kmph$.