Question

A train travels 360 km at a uniform speed.if the speed had been 5km/h more,it would have taken 1 hour less for the same journey.find the speed of the train

Answer 1

Answer:

=) 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 (x+5-x)/x(x+5) = 1

⇒360 (5) = x^2 + 5x

⇒1800 = x^2 + 5x

⇒x^2 + 5x - 1800 = 0

⇒x^2 + 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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Answer 2

Answer:

Step-by-step explanation:

Solution :-

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

Time taken to cover 360 km =  360/x hr

Time taken to cover 360 km at new speed = 360/x + 5 hr

According to the Question,

⇒ 360/x - 360/ x + 5 = 1

⇒ 360 (x + 5 - x)/x(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 (Speed cannot be negative)

⇒ x = 40 km/hr.

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