# Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is?**

The rate of change of velocity refers to the derivative of velocity with respect to time. In other words, it measures how quickly an object’s velocity is changing over time. The ratio of the speed of the two trains will be 3:2.

Table of content

## What is The Rate Of Change Of Velocity?

The rate of change of velocity is represented as the derivative of velocity (v) with respect to time (t) and is denoted as dv/dt or Δv/Δt, where Δv represents the change in velocity and Δt represents the change in time.

The rate of change of velocity can be positive, negative, or zero, depending on whether the velocity is increasing, decreasing, or remaining constant over time.

**a = Δv / Δt**

*Where:*

**a**represents acceleration**Δv**represents the change in velocity (final velocity – initial velocity)**Δt**represents the change in time (final time – initial time)

**For Example:** if an object’s velocity changes from 10 meters per second (m/s) to 20 m/s in 5 seconds, the rate of change of velocity would be (20 m/s – 10 m/s) / 5 s = 2 m/s². This means the velocity is increasing at a rate of 2 meters per second squared.

**Solution**

Let the speeds of the two trains be x m/sec and y m/sec, respectively.

The length of the first train is given as 27x meters and the length of the second train is 17y meters.

The time taken for the two trains to cross each other is given as 23 seconds, so we can set up the equation:

27x+17y/x+y = 23

To solve this equation, we simplify it:

27x+17y = 23x+23y

Rearranging the equation:

27x−23x = 23y−17y

4x = 6y

Now, we can find the ratio of the speeds of the two trains

x/y = 3/2

Therefore, the ratio of the speeds of the two trains is 3:2.

**Summary**

## Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is?

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speed is 3:2.

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