Calculating Train Speed for a Given Distance

This article discusses the process of determining the required speed of a train to cover a predetermined distance within a specified time frame. Additionally, we examine a scenario involving train speed and explore the underlying principles of distance, speed, and time.

Imagine a train traveling at a consistent average speed of 100 km/h over a period of 3 hours and 36 minutes. The objective is to calculate the required average speed for the train to cover the same distance in 2 hours and 30 minutes. This problem highlights the importance of understanding the relationship between distance, speed, and time, and how these factors are interconnected in solving various real-world problems.

Step-by-Step Solution

To solve this problem, we will follow these steps:

Calculate the Distance: Given that the train travels for 3 hours and 36 minutes at a speed of 100 km/h, the first step is to convert the time into hours and then use the formula Distance Speed × Time to find the distance. Calculate the Required Speed for the Second Scenario: This step involves using the calculated distance and the new time to find the required speed for the train to cover the same distance in the given time.

Step 1: Calculate the Distance

First, we convert 3 hours and 36 minutes into hours:

3 hours (36 minutes ÷ 60) 3 hours 0.6 hours 3.6 hours

Next, we use the formula:

Distance Speed × Time

The distance covered by the train is:

Distance 100 km/h × 3.6 hours 360 km

Step 2: Calculate the Required Speed for the Second Scenario

Now, we need to determine the average speed required to cover the same distance of 360 km in 2 hours and 30 minutes.

First, we convert 2 hours and 30 minutes into hours:

2 hours (30 minutes ÷ 60) 2 hours 0.5 hours 2.5 hours

Using the formula for speed:

Speed Distance ÷ Time

The required speed is:

Speed 360 km ÷ 2.5 hours 144 km/h

Conclusion

The train must travel at an average speed of 144 km/h to cover the same distance in 2 hours and 30 minutes. This problem underscores the importance of accurate calculations and the application of basic physics principles in solving real-world problems.

Moreover, it is crucial to note that the car can cover the same distance at any speed as long as it is not zero. This point emphasizes the flexibility in speed but the necessity of covering a specific distance within a given timeframe.

For a more precise calculation, another solution might be:

Calculate the Distance: Given that the train travels for 3 hours 25 minutes at 100 km/h, the distance covered is: d 100 km/h × (3 25/60) hours 341.667 km Using the second scenario, with 2 hours 30 minutes, the required speed is: v 341.667 km ÷ (2.5 hours) 136.667 km/h

Finally, using a more mathematical approach:

d1 d2 100 km v1 100 km ÷ (3 25/60) hours 29.27 km/h t2 2 30/60 hours 2.5 hours v2 100 km ÷ 2.5 hours 40 km/h The final calculation is: v (100 × 3 20/60) ÷ (2 30/60) 125 km/h

These steps and solutions demonstrate the various methods to arrive at the required speed for a given distance and time.