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A train 360 km at a uniform speed. If the speed had been 10 km/h more, it would have taken 3 hours less for the same journey. What is the speed of the train (in km/h)?

A train 360 km at a uniform speed. If the speed had been 10 km/h more, it would have taken 3 hours less for the same journey. What is the speed of the train (in km/h)? Correct Answer 30

Let the original speed of the train be x km/h.

Time taken to cover a distance of 360 km = 360/x hours.

New speed of the train = (x + 10) km/h.

Time taken to cover a distance of 360 km at new speed = 360/(x + 10) hours.

Since, the train takes 3 hour less time,

∴ 360/x - 360/(x + 10) = 3

⇒ 360 (x + 10 - x)/x(x + 10) = 3

⇒ 120 × 10 = x2 + 10x

⇒ 1200 = x2 + 10x

⇒ x2 + 10x - 1200 = 0

⇒ x2 + 40x - 30x - 1200 = 0

⇒ x (x + 40) - 30( x + 40) = 0

⇒ (x + 40) (x - 30) = 0

⇒ x = (- 40), 30

But speed can not be in negative.

∴ x = 30 km/hr.

Hence, the original speed of the train is 30 km/h.

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