Question

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

Answer 1

Answer:

Your answer

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Answer 2

Answer:

$Given distance=360 km. Let the speed of the train be x km/hr.Speed when increased by 5 km/hr =(x+5) km/hrx360​ − (x+5)360​ =1x(x+5)[360x+1800−360x]​ =1x 2 +5x−1800=0x 2 +45x−40x−1800=0x(x+45)−40(x+45)=0(x−40)(x+45)=0x=40,−45The speed of the train is 40 km/hr.$

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 (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.