Question

A train travels a distance of 300 km at a uniform speed. if the speed of the train is increased by 5km per hour,the journey would have taken two hours less. find the original speed of the train

Answer 1

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Answer 2

Step-by-step explanation:

Solution :-

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

Time taken by train to cover = 300/x hrs.

Increased speed = 5 km/h

Time taken to cover 300 km when speed is increased = 300/(x + 5) hrs.

According to the Question,

⇒ 300/x - 300/(x + 5) = 2

⇒ 300(x + 5) - 300x/x(x + 5) = 2

⇒ 300x + 1500 - 300x/x² + 5x = 2

⇒ 2x² + 10x = 1500

⇒ x² + 5x - 750 = 0

By using factorization method, we get

⇒ x² + 30x - 25 - 750 = 0

⇒ x(x + 30) - 25(x + 30) = 0

⇒ (x + 30) (x - 25) = 0

⇒ x + 30 = 0 or x - 25 = 0

⇒ x = - 30, 25 (As x can't be negative)

⇒ x = 25 km/h

Hence, the original speed of train is 25 km/h

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