Поезд Проехал 690 Км. Расчет Скорости На Разных Участках Пути

This article will delve into a classic problem involving distance, speed, and time, focusing on a train journey of 690 kilometers. We will break down the problem step-by-step to understand how to calculate the speed of the train during different segments of its journey. This is a fundamental concept in mathematics and physics, often encountered in everyday situations and standardized tests. Understanding the relationship between distance, speed, and time is crucial for solving various real-world problems, such as planning travel itineraries, estimating arrival times, and analyzing motion. This article aims to provide a clear and concise explanation of the concepts involved and guide you through the solution process. We'll use the basic formula: distance = speed × time (d = s × t), which is the cornerstone of solving such problems. By rearranging this formula, we can also calculate speed as distance divided by time (s = d / t) and time as distance divided by speed (t = d / s). These variations will be essential in our calculations.

The Problem: A Breakdown

The problem states that a train traveled a total distance of 690 kilometers. The journey is divided into two parts. For the first 8 hours, the train traveled at a speed of 70 kilometers per hour. The remaining part of the journey was completed in 2 hours. The question asks us to find the speed of the train during this remaining part of the journey. To solve this problem, we need to first determine the distance covered in the first part of the journey. Then, we will subtract this distance from the total distance to find the distance covered in the second part of the journey. Finally, we will use the formula speed = distance / time to calculate the speed during the second part of the journey. This step-by-step approach will help us break down the complex problem into smaller, manageable parts, making it easier to understand and solve. We'll also emphasize the importance of understanding the units of measurement (kilometers, hours, kilometers per hour) and how they relate to each other in the calculations. Accurate use of units is crucial for obtaining the correct answer.

Step 1: Distance Covered in the First 8 Hours

In this section, let's calculate how far the train traveled in the initial 8 hours of its journey. We know the train's speed during this period was a constant 70 kilometers per hour. To determine the distance covered, we will apply the fundamental formula: distance = speed × time. In our case, the speed is 70 km/h, and the time is 8 hours. Substituting these values into the formula, we get: Distance = 70 km/h × 8 h. Multiplying these values, we find that the distance covered in the first 8 hours is 560 kilometers. This calculation is a direct application of the relationship between distance, speed, and time. It's important to note that the units are consistent: kilometers per hour multiplied by hours gives kilometers, which is the unit of distance. This first step is crucial because it allows us to break down the problem into smaller parts. We now know the distance covered in the first segment of the journey, which will help us determine the distance covered in the remaining segment. This step highlights the importance of carefully extracting the given information from the problem statement and using it in the appropriate formula. This calculation demonstrates a core principle in physics and mathematics: the relationship between distance, speed, and time is fundamental to understanding motion and solving related problems. Mastering this relationship is essential for tackling more complex problems involving varying speeds and times.

Step 2: Distance Covered in the Remaining 2 Hours

Having calculated the distance covered in the first part of the journey, our next task is to find the distance the train traveled in the remaining 2 hours. We know the total distance of the journey is 690 kilometers, and we've already determined that the train covered 560 kilometers in the first 8 hours. To find the distance covered in the last 2 hours, we simply subtract the distance covered in the first 8 hours from the total distance. This can be expressed as: Distance (remaining) = Total distance - Distance (first 8 hours). Substituting the values, we have: Distance (remaining) = 690 km - 560 km. Performing the subtraction, we find that the train covered 130 kilometers in the remaining 2 hours. This step is a straightforward application of subtraction and demonstrates how we can use previously calculated values to solve subsequent parts of the problem. It highlights the importance of breaking down a complex problem into smaller, manageable steps. By finding the distance covered in the remaining 2 hours, we have crucial information needed to calculate the train's speed during that segment of the journey. This subtraction step is a key link in the chain of calculations that leads us to the final answer. It reinforces the idea that understanding the relationships between different quantities, such as total distance and partial distances, is essential for problem-solving.

Step 3: Calculating the Speed During the Last 2 Hours

Now that we know the distance covered in the last 2 hours (130 kilometers), we can calculate the train's speed during this part of the journey. We will again use the formula: speed = distance / time. In this case, the distance is 130 kilometers, and the time is 2 hours. Substituting these values into the formula, we get: Speed = 130 km / 2 h. Performing the division, we find that the speed of the train during the last 2 hours was 65 kilometers per hour. This calculation is a direct application of the speed formula and demonstrates how we can use distance and time to determine speed. The units are consistent: kilometers divided by hours gives kilometers per hour, which is the unit of speed. This step represents the culmination of our problem-solving process. We have used the given information and the calculated values from previous steps to arrive at the final answer. It emphasizes the importance of careful calculation and attention to units. The result, 65 km/h, gives us a clear understanding of the train's speed during the final leg of its journey. This step underscores the practical application of mathematical concepts in real-world scenarios, such as calculating speeds and distances in transportation.

Solution

The speed of the train during the remaining part of the journey was 65 kilometers per hour. This solution was reached by breaking the problem down into three key steps: calculating the distance covered in the first 8 hours, determining the distance covered in the remaining 2 hours, and finally, using the distance and time of the final leg to calculate the speed. This step-by-step approach demonstrates a valuable problem-solving strategy: breaking down a complex problem into smaller, more manageable parts. By addressing each part individually, we can build towards the solution systematically. The problem also illustrates the fundamental relationship between distance, speed, and time, and how these concepts can be applied to real-world situations. The final answer, 65 km/h, provides a clear and concise solution to the original question. This solution reinforces the importance of careful calculation and the correct application of formulas. It also highlights the practical relevance of mathematics in understanding and analyzing motion.

Problem: The train traveled 690 km. The first 8 hours it traveled at a speed of 70 km/h. It traveled the rest of the way in 2 hours. What speed did the train travel the rest of the way?