Determining the Total Length of a Post Embedded in Mud, Water, and Air

Understanding the total length of a post when a fraction of its length is in mud, another fraction is in water, and the remainder is above the water can be a practical exercise in problem-solving. In this article, we explore a step-by-step approach to finding the total length of such a post. This problem involves fractions, algebraic manipulation, and logical reasoning, all of which are fundamental skills in mathematics.

Problem Statement

The problem states that a post has 1/4 of its length in the mud, 1/3 of its length in water, and 15 meters above the water. We need to find the total length of the post.

Step-by-Step Solution

Step 1: Represent the lengths as fractions of the total length

Let the total length of the post be L. According to the problem:

1/4 L is in the mud. 1/3 L is in the water. The remaining length, 15 meters, is above the water.

Step 2: Set up the equation

We can express the total length of the post as the sum of these three parts:

Span style"font-size: 18px;">L 1/4 L 1/3 L 15

Step 3: Combine the fractions

To solve the equation, we first need to combine the fractions. The least common multiple of 4 and 3 is 12. So we can rewrite the fractions as:

1/4 L 3/12 L

1/3 L 4/12 L

Step 4: Simplify the equation

Substituting these back into the equation gives:

3/12 L 4/12 L 15 L

Combining the fractions:

7/12 L 15 L

Step 5: Isolate L

Next, we isolate L by subtracting 7/12 L from both sides:

15 L - 7/12 L

This simplifies to:

15 5/12 L

Step 6: Solve for L

To solve for L, we multiply both sides by 12/5:

L 15 x 12/5 36 meters

Conclusion

The total length of the post is 36 meters. This problem demonstrates the application of basic algebra and problem-solving techniques to solve a practical scenario.

Additional Tips

1. Always check that the combination of fractions covers the entire length of the post (i.e., 12/12).

2. Make sure to properly handle the units (meters, in this case).

3. Practice similar problems to improve your skill in decomposing and combining mathematical expressions.

Related Keywords

Length Calculations: Understanding and calculating lengths in various contexts.

Problem-Solving Techniques: Applying logical and mathematical methods to solve real-world problems.

Mathematical Modeling: Representing real-world scenarios using mathematical expressions and equations.