# A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

By Ritesh|Updated : November 13th, 2022

The original average speed is 42 km/hr. Steps to find the original average speed:

Let x represent the train's initial average speed. The time required by the train to travel 63 km at the original speed is equal to 63/x.

Time is taken by train to cover 72 km with increased speed = 72/ (x + 6)

According to the question it is given:

63/x + 72/ (x + 6) = 3

[63 (x + 6) + 72x]/x (x + 6) = 3

[63x + 378 + 72x]/(x2 + 6x) = 3

In simplification we get the:

378 + 135x = 3x2 + 18x

3x2 - 117x - 378 = 0

x2 - 39x - 126 = 0

x2 - 42x + 3x - 126 = 0

Taking common we get:

x (x - 42) + 3 (x - 42) = 0

(x + 3) (x - 42) = 0

We get:

x = 42, -3

Since speed cannot be zero, the initial average speed is 42 km per hour.

### Forms of Speed

There are four different forms of speed:

• When an object moves over the same distance in the same length of time, it is said to be traveling at a constant speed.
• An object is considered to be traveling at a varied pace when it covers a varying distance at regular intervals.
• The ratio of the total distance an object has traveled to the total amount of time it has taken to cover that distance is used to calculate average speed.
• Instantaneous speed: An object's instantaneous speed is the speed it is moving at any given time when moving at a variable speed.

Summary:

## A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, its original average speed is 42km/hr.