Question

A train travel 360km at uniform speed. If the speed had been 5km /hr more, it would have taken 1hr less. Find the speed of train.

Answer 1

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

Taking 360 outside;

=360[(1/x)-(1/x+5)]

⇒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 you understand

Thank you :)