Question

The 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:

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 will help u

Answer 2

$\huge{\boxed{\mathcal{ANSWER}}}$

Total Distance = 360 km

Let, the speed of the train be ' x ' km.

Original time = 360/x hour

Speed is increased = 5km/h

Total time = 360/x+5 hour

Now, According to the Question :

360/x - 360/x+5 = 1

Now we have to solve this, then we get :

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

1/x - 1/x+5 = 1/360

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

x+5-x/x² + 5x = 1/360

x² + 5x = 360x + 1800 - 360x

x² + 5x - 1800 = 0

∴ This is the required equation and this also we have to solve by middle term splitting method for getting the speed of the train.

x² + 5x - 1800 = 0

x² + 45x - 40x - 1800 = 0

x (x+45) - 40( x +45) = 0

(x+45) (x-40) = 0

x + 45 = 0  or  ,  x - 40 = 0

x = - 45     or  ,  x = 40

• Note, that point that speed never be in Negative.

$\implies\boxed{\mathsf{Hence,\:the\:original\:speed\:of\:the\:train\:be\:x\:=\:40\:km/hr}}}$