Question

A train travels from station X to station Y with a speed of 40Km/hr and returns with a speed of 50Km/hr then average speed of total journey is *​

Answer 1

Answer:

Average speed = 400/9 km/h

Explanation:

As per the information provided in the question, We have :

• A train travels from station X to station Y with a speed of 40Km/hr and returns with a speed of 50Km/hr.

We are asked to find the average speed of the total journey.

In order to find the average speed, We need to find total distance covered and total time taken by the train to travel a certain distance.

Let the Distance between x and y be z.

Finding time taken :

$\longmapsto \bf Time _ {(Total)} = Time _{(from \: X \: to \: Y)} + Time _ {(from \: Y \: to \: X)}$

As we know that,

• Time = Distance/Speed. So,

$\longmapsto \rm Time _ {(Total)} = \dfrac{z}{40} + \dfrac{z}{50}$

$\longmapsto \rm Time _ {(Total)} = \dfrac{9z}{200}$

∴ The total time taken is 9z/200.

Finding total distance :

As, The distance between X and Y is z. The distance in travelling and again returning will be 2z.

Finding average speed :

$\longmapsto \bf Average\; speed = \dfrac{Total\; distance}{Total\; time}$

Putting the values,

$\longmapsto \rm Average\; speed = \dfrac{2z}{ \dfrac{9z}{200} }$

$\longmapsto \rm Average\; speed = 2z \times \dfrac{200}{9z}$

$\longmapsto \rm Average\; speed = \dfrac{400z}{9z}$

$\longmapsto \rm Average\; speed = \dfrac{400}{9}$

∴ Average speed of the train is 400/9 km/hr.