Determining the Speed of a Goods Train Using Train Overtake Problems

Introduction

Understanding speed and distance relations in train overtake problems is a fundamental concept in physics and engineering. This article will explore how to determine the speed of a goods train, given the speed of a passenger train, the time delay in departure, and the overtaking time. These calculations are crucial for logistical planning and optimization in railway operations.

Problem Statement

Problems:

1. A passenger train running at a speed of 80 km/h leaves a railway station 6 hours after a goods train leaves and overtakes it in 4 hours. What is the speed of the goods train?

2. A passenger train running at a speed of 90 km/h leaves the station 6 hours after a goods train leaves and overtakes it in 4 hours. What is the speed of the goods train?

Solution for Problem 1

We can utilize the distance-speed-time relationship to solve the given problem. Let's break down the steps to find the speed of the goods train.

Step 1: Determine the distance traveled by the passenger train

The passenger train travels for 4 hours at a speed of 80 km/h:

text{Distance}_{text{passenger}} 80 times 4 320 text{ km}

D_{text{passenger}} 320 text{ km}

Step 2: Calculate the time traveled by the goods train

The goods train leaves 6 hours before the passenger train. During the 4 hours it takes for the passenger train to overtake the goods train, the goods train has been traveling for 10 hours in total:

T_{text{goods}} 10 text{ hours}

Step 3: Set up the equation for the goods train speed

Let the speed of the goods train be ( v ) km/h. The distance covered by the goods train in 10 hours is:

10v 320 text{ km}

10v 320

Step 4: Solve for ( v )

Dividing both sides of the equation by 10, we get:

v frac{320}{10} 32 text{ km/h}

v 32 text{ km/h}

Conclusion:

The speed of the goods train is 32 km/h.

Solution for Problem 2

Following a similar method, let's solve the second problem using the given data:

A passenger train running at a speed of 90 km/h leaves the station 6 hours after a goods train leaves and overtakes it in 4 hours. We need to determine the speed of the goods train.

Step 1: Determine the distance traveled by the passenger train

The passenger train travels for 4 hours at a speed of 90 km/h:

D_{text{passenger}} 90 times 4 360 text{ km}

Step 2: Calculate the total time traveled by the goods train

Similarly, the goods train travels for a total of 10 hours (6 hours before the passenger train starts plus 4 hours until it is overtaken):

T_{text{goods}} 10 text{ hours}

Step 3: Set up the equation for the goods train speed

Let the speed of the goods train be ( S ) km/h. The distance covered by the goods train in 10 hours is:

S times 10 360 text{ km}

S times 10 360

Step 4: Solve for ( S )

Dividing both sides of the equation by 10, we get:

S frac{360}{10} 36 text{ km/h}

S 36 text{ km/h}

Conclusion:

The speed of the goods train is 36 km/h.

Conclusion

This article has provided a detailed solution to the train overtake problems, demonstrating the application of the distance-speed-time relationship. Understanding these concepts is crucial for railway and logistics management, where precise calculations of speed and distance can significantly impact operational efficiency and safety.

Keywords

Speed Calculation, Train Overtake, Distance Relation