Question

In a journey of \(1560 \mathrm{km},\) a person traveled \(195 \mathrm{km}\) by car and the rest of the distance by rail. What percent of the distance was traveled by rail?

Short answer

The person traveled 87.5% of the distance by rail.

Step-by-step solution

Find the Distance Traveled by Rail

To find the distance traveled by rail, subtract the distance traveled by car from the total distance of the journey.

Calculate the Percentage Traveled by Rail

Divide the distance traveled by rail by the total distance and multiply by 100 to find the percentage.

Key concepts

Mathematical Problem Solving

At the heart of conquering mathematical challenges is the ability to engage in systematic problem solving. When approaching percentage problems or any other mathematical scenario, it's crucial to start by understanding the question and identifying the information given. Understanding the problem allows you to determine the steps needed to find the solution.

In the given exercise, the problem solving process is initiated by identifying that the total journey distance and the part of the journey covered by car are both known quantities. The next step is determining what needs to be found – the percentage of distance traveled by rail. This is followed by a two-step solution, which involves first finding the actual distance covered by rail and then calculating this distance as a percentage of the total journey. The systematic approach, starting with data extraction and proceeding to calculation, simplifies complex problems into solvable steps.

Distance Calculations

Calculating distance is fundamental in various fields, including mathematics and geography. In the given task, an understanding of distance calculations is vital. The first part of solving our exercise involves a subtraction to find the distance traveled by rail: subtracting the distance covered by car from the total distance.

To properly visualize this: if one imagines the total journey as a long strip of road, a segment of this road equivalent to 195 km is taken up by car travel. The remaining stretch represents rail travel. Thus, the task requires subtracting the car's segment from the whole to understand what fraction remains for the rail part of the journey: \[1560 \text{ km} - 195 \text{ km} = 1365 \text{ km (by rail)}.\] Distance calculations like these often serve as intermediate steps in broader problem-solving tasks.

Percentage Calculation

Understanding percentage calculation is essential for interpreting data in terms of proportions, which is a common requirement across various disciplines. In our example, once the distance traveled by rail is known (1365 km), we proceed to calculate this as a percentage of the total journey distance (1560 km).

This percentage represents the proportion of the journey completed by rail. The formula used is: \[\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\%\]. In applying this formula to our exercise, the calculation becomes: \[\text{Percentage by rail} = \left(\frac{1365}{1560}\right) \times 100\% \approx 87.5\%\]. This figure, 87.5%, signifies that the majority of the journey was made by rail. By mastering percentage calculations, students can better understand and express quantitative relationships in an easily interpretable format.