Solving a Distance Problem: A Comprehensive Guide for SEO

When faced with a complex mathematical problem, such as determining the total distance traveled by a car, it's essential to break down the solution into manageable steps. This article aims to walk you through a practical example, explaining the problem-solving process and providing actionable insights for improving SEO content related to mathematics and algebra.

Introduction to the Problem

Consider the following problem: A car covered one quarter of the entire distance in the first hour, one fifth in the second hour, and one sixth in the third hour. There are still 115 km to go. How far should the car travel?

Step-by-Step Solution

To solve this problem, we can use algebraic methods. Here’s a detailed step-by-step guide:

Step 1: Identify the Fractions of the Distance

The car covered the following distances in the first three hours:

1/4 of the distance in the first hour 1/5 of the distance in the second hour 1/6 of the distance in the third hour

Let the total distance be (D).

Step 2: Express the Coveraged Distances in Terms of (D)

The distance covered in the first hour: ( frac{D}{4} )

The distance covered in the second hour: ( frac{D}{5} )

The distance covered in the third hour: ( frac{D}{6} )

The total distance covered in the first three hours is:

Step 3: Determine the Total Distance

The problem states that the remaining distance is 115 km. Thus, the remaining distance can be expressed as:

Remaining distance: ( D - left( frac{D}{4} frac{D}{5} frac{D}{6} right) 115 )

Step 4: Simplify the Equation

First, find the least common multiple (LCM) of 4, 5, and 6, which is 60.

Convert each fraction to have a common denominator:

( frac{D}{4} frac{15D}{60} )

( frac{D}{5} frac{12D}{60} )

( frac{D}{6} frac{10D}{60} )

Now, add these terms:

( frac{15D}{60} frac{12D}{60} frac{10D}{60} frac{37D}{60} )

So, the equation becomes:

( D - frac{37D}{60} 115 )

Which simplifies to:

( frac{23D}{60} 115 )

To find (D), multiply both sides by 60/23:

( D 115 times frac{60}{23} )

Calculate the value:

( D frac{115 times 60}{23} 300 ) km

Conclusion

The total distance the car should travel is 300 km. This problem demonstrates the importance of breaking down complex problems into simpler steps and using algebra to solve them.

SEO Tips for Academic Content

When writing content related to mathematics and algebra for public consumption, it's crucial to optimize the page for search engines. Here are some SEO tips:

Keyword Integration

Use the target keywords, such as "math problem solving" and "distance calculation," organically throughout the content. This will help improve search rankings.

Maintain Readability

Ensure that the content is easy to read by using short, informative paragraphs and breaking down complex problems into manageable steps.

Utilize Visual Aids

Incorporate diagrams, equations, and visual aids to help clarify the concepts and make the content more engaging.

Implement Structured Data

Use structured data markup to provide search engines with structured information about the page, such as the topic, keywords, and solution method.

Conclusion

By understanding how to break down complex mathematical problems and optimize content for SEO, you can provide valuable resources to your audience and improve the visibility of your content on search engines.