A train takes $$2\frac{1}{2}$$ hours less for a journey of 300 km, if its speed is increased by 20 km/h from its usual speed. How much time will it take to cover a distance of 192 km at its usual speed?

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