Question

A train travels 360 km at a uniform speed if the speed had been 5 km per hour more it would have taken 1 hour less for the same journey find the speed of the train​

Answer 1

original speed is 40km/hr

Answer 2

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Let the original speed of train = x km/hr

Distance = 360 km

So ,

TiMe = Distance / speed

Now,

New speed of the train = (x+5) km/hr

Time = 360/(x+5)

ACcording to statement :

$= > \frac{360}{x} - \frac{360}{x + 5} = 1 \\ \\ = > \frac{360(x + 5) - 360(x)}{x(x + 5)} = 1 \\ \\ = > \frac{360x + 1800 - 360x}{ {x}^{2} + 5x } = 1 \\ \\ = > 1800 = {x}^{2} + 5x \\ \\ = > {x}^{2} + 5x - 1800 = 0 \\ \\ = > {x}^{2} + 45x - 40x - 1800 = 0 \\ \\ = > x(x + 45) - 40(x + 45) = 0 \\ \\ = > (x - 40)(x + 45) = 0 \\ \\ = > x = - 45 ,\: 40$

But since speed cannot be in negative.

∴ x = 40 km/hr.

Hence, the original speed of the train is 40 km/h.

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