Explanation:

Let the usual peed of train be x km/hr.
Distance = 300 km
Time = $$2\frac{1}{2}$$ hours = $$\fra{5}{2}$$ = 2.5 hr
Time = distance/speed
According to quetion,
$$\frac{300}{x} - \frac{300}{x + 20} = 2.5$$
$$(x + 20) \times 120 - 120x = x(x + 20)$$
$$120x + 2400 - 120x = x^2 + 20x$$
$$x^2 + 20x - 2400 = 0$$
$$x^2 + 60x - 40x - 2400 = 0$$
$$x(x + 60) - 40(x + 60) = 0$$
$$(x + 60)(x- 40) = 0$$
x = 40
Distance = 192 km
Time taken to cover distance by usually speed = 192/40 = 4.8 hours