Train travels at 3 hours if it's speed is 65 miles per hour. It takes the train 2.5 hours if it's speed is 78 per hour . Identify the variation type

Step-by-step explanation:

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+5) km/h.

Time taken to cover a distance of 360 km at new speed = 360/x+5 hours.

Since, the train takes 1 hour less time,

∴360/x - 360/ x+5 = 1

⇒360 (5) = x² + 5x

⇒1800 = x² + 5x

⇒x² + 5x - 1800 = 0

⇒x² + 45x - 40x - 1800 = 0

⇒x (x+45) - 40( x +45) = 0

⇒(x+45) (x-40) = 0

⇒x = (-45), 40

But since speed cannot be in negative.

∴x = 40 km/hr.

Hence, the original speed of the train is 40 km/h.

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Step-by-step explanation:

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