A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Given distance = 360 km

Consider x as the speed, then the time taken

t =$\frac{360}{x}$

If the speed is increased by 5 km/h, new speed will be (x + 5) km/h

Distance will be the same

t = $\frac{360}{x+5}$

We know that

Time with original speed – Time with increased speed = 1

$\frac{360}{x}$ – $\frac{360}{x+5}$ = 1

$\frac{360(x+5)-360x}{x(x+5)}$ = 1

360x + 1800 – 360x = x(x + 5)

x² + 5x = 1800

x² + 5x – 1800 = 0

x² + 45x – 40x – 1800 = 0

x(x + 45) – 40(x + 45) = 0

(x – 40)(x + 45) = 0

x = 40 km/hr

As we know, the value of speed cannot be negative.

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