Question

A Train travel 180 km at a uniform speed if the speed had been 9 km/hour more it would have taken I hour less for the same journey find the speed of the train​

Answer 1

Answer:

Let the speed of the train be xkmph

The time taken by the train to travel 180km is =

$\frac{180}{x}h$

The increased speed is x + 9

The time taken is

$\frac{180}{x + 9}$

According to the question,

The time taken is

$\frac{180}{x} - 1$

$= \frac{180}{x} - 1 = \frac{180}{x - 9}$

$= \frac{180 - x}{x} = \frac{180}{x + 9}$

$= 180x - {x}^{2} + 1680 - 9x = 180x$

$= {x}^{2} - 9x - 1680 = 0$

$= {x}^{2} + 45x - 36x - 1680 = 0$

$= x(x + 45) - 36(x + 45) = 0$

X = 36, -45

Speed cannot be negative (in this case,)

So the speed of the train is 36kmph

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