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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.

Q8.    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.

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Let the speed of the train be x\ km/hr.

Then, time taken to cover 360km will be: 

=\frac{360}{x}\ hr

According to the question,

\Rightarrow (x+5)\left ( \frac{360}{x}-1 \right ) = 360

\Rightarrow 360-x+\frac{1800}{x} - 5 = 360

Making it a quadratic equation.

\Rightarrow x^2+5x-1800 = 0

Now, solving by the factorizing method:

\Rightarrow x^2+45x-40x-1800 = 0

\Rightarrow x(x+45)-40(x+45) = 0

\Rightarrow (x-40)(x+45) = 0

\Rightarrow x = 40,\ -45

However, the speed cannot be negative hence,

The speed of the train is 40\ km/hr.

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