Question

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

Answer 1

Answer:

Explanation:

Solution :-

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

Time taken to cover 360 km = 360/x h

Time taken to cover km with the speed of (x + 5) km/h = 360/x + 5

According to the Question,

⇒ 360/x - 360/x + 5 = 1

⇒ 360(x + 5) - 360x/x(x + 5) = 1

⇒ 360x + 1800 - 360x/x(x + 5) = 1

⇒ x² + 5x - 1800 = 0

⇒ x² + 45x - 40x - 1800 = 0

⇒ x(x + 45) - 40(x + 45) = 0

⇒ (x + 45) (x - 40) = 0

⇒ x = - 45, 40 (Neglecting negative sign)

⇒ x = 40 km/h

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

Answer 2

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) = 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.

hope it helps u