Question

A train travel 360 km at uniform speed.it the speed had been 5 kms/hr more,it would have taken 1 hour less for the same journey.find the speed of the train​

Answer 1

Let the speed of the train = x km/h

increase speed of the train = (x+5)km/h

distance travelled by the train = 360km

time taken by the train = D/S=360/x hours

time taken by the train with increased speed = 360/x+5 hrs.

now according to condition

360/x - 360/x+5 = 1

360(x+5) - 360x = x(x+5)

360x + 1800 - 360x = xsquare + 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

Now x+45= 0 or x-40 = 0

x = -45(Rejected) or x = 40

as speed cannot be 0 therefore, speed of the train = 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) = 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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