Question

A 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

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.

Answer 2

Answer:

40 km / hr

Step-by-step explanation:

Let uniform speed of train = p km / hr

= > Increased speed = p + 5 km / hr .

We have given total distance = 360 km

We know :

Speed = Distance / Time :

= > T = D / S

Time at uniform speed t₁ :

= > t₁ = ( 360 / p ) hr

Time at increased speed t₂ :

= > t₂ = ( 360 / p + 5 ) hr

Since as we know : s ∝ 1 / t

= > t₁ - t₂ = 1

Putting values here we get :

= >  ( 360 / p ) -  ( 360 / p + 5 ) = 1

= > ( 1 / p ) - ( 1 / p + 5 ) = 1 / 360

= > ( p + 5 - p ) / ( p ) ( p + 5 ) = 1 / 360

= > 1 / ( p² + 5 p ) = 1 / 1800

= > p² + 5 p - 1800 = 0

= > p² + 45 p - 40 p + 1800 = 0

= > ( p + 45 ) ( p - 40 ) = 0

= > p = 40  OR  p = - 45

Since speed is scalar quantity , it can't be negative!

Therefore , speed of the train is 40 km / hr.