Question

A train travels 260 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.

Answer 2

Given :  A train travels 260 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

To find : the original speed of the train.

Solution:

A train travels 260 km at a uniform speed.

=> Distance =   260 km

Let say original uniform Speed   of Train = T  km/hr

Time taken   = 260/ T  hr

If the speed had been 5 km/h more, it would  have taken 1 hour less for the same journey.

Time taken with  5 km/h more speed = 260/(T + 5)

( 260/ T)   -  1  =  260/(T + 5)

=> 260 ( T + 5)   - T(T + 5) = 260T

=> 260T  + 1300 - T²  - 5T = 260T

=> T² + 5T - 1300  = 0

=> T  =( -5  ± √5² - 4(-1300) ) /2        

( -ve value of speed  not possible , hence ignored)

=> T  = ( -5  + √5225 ) /2  

=> T = 33.64 km /hr

Original Speed of Train = 33.64 km/hr

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