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in Quadratic Equations by (65.5k points)

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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by (65.2k points)
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Best answer

Let initial speed of the train be x km/h, 

Then, time taken to cover 360 km 

If the speed had been 5 km/h more, \(\frac{360}{x}\)Hr. 

then time taken to cover is \(\frac{360}{x + 5}\) Hr.

x(x + 365) = 360 (x + 5) 

x2 + 365x = 360x + 1800 

x2 + 365x – 360x – 1800 = 0 

x2 + 5x – 1800 = 0 

x2 + 45x – 40x – 1800 = 0 

x(x + 45) – 40 (x + 45) = 0 

(x + 45) (x – 40) = 0 

If x + 45 = 0, then x = – 45 

If x – 40 = 0, then x = 40 

∴ Initial speed of a train is 40 km/hr.

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