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 BYJU'S Exam Prep

Updated on: September 25th, 2023

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 = 3×2 + 18x

3×2 – 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.

Table of content

1. 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?

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: