50
A faster train takes one hour less than a slower train for a journey of $200$ km. If the speed of the slower train is $10$ km/hr less than that of the faster train, find the speeds of the two trains.
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Let the speed of faster train be $x$ km/h
$\therefore$ speed of slower train $= (x – 10)$ km/h
According to the question,
$\frac{200}{x-10} - \frac{200}{x} = 1$ (I) (2 Marks)
$\Rightarrow x^2 - 10x - 2000 = 0$ (II) (1 Mark)
$\Rightarrow (x - 50)(x + 40) = 0$ (III) (1 Mark)
$\therefore x = 50$
$x = -40$ (Rejected) (IV) (1/2 Mark)
Hence, speed of faster train $= 50$ km/h
and speed of slower train $= 40$ km/h (V) (1/2 Mark)
$\therefore$ speed of slower train $= (x – 10)$ km/h
According to the question,
$\frac{200}{x-10} - \frac{200}{x} = 1$ (I) (2 Marks)
$\Rightarrow x^2 - 10x - 2000 = 0$ (II) (1 Mark)
$\Rightarrow (x - 50)(x + 40) = 0$ (III) (1 Mark)
$\therefore x = 50$
$x = -40$ (Rejected) (IV) (1/2 Mark)
Hence, speed of faster train $= 50$ km/h
and speed of slower train $= 40$ km/h (V) (1/2 Mark)