A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Let the first speed of the train be x km/h

Time taken to cover 54 km =

New speed of train = x + 6 km/h

Time taken to cover 63 km =

According to given question

⇒

⇒
Taking LCM

⇒ 117x + 324 = 3(x2 + 6x)

⇒ 117x + 324 = 3x2 + 18x

⇒ 3x2 – 99x – 324 = 0

⇒ x2 – 33x – 108 = 0

⇒ x2 – 36x + 3x – 108 = 0

⇒ x (x – 36) + 3(x – 36) = 0

⇒ (x – 36) (x + 3) = 0

⇒ x = 36 or x = – 3

⇒ x = 36 (speed cannot be negative)

Hence the first speed of the train is 36 km/hr

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