Mariela's Journey: Calculating Total Distance In Meters

Hey guys! Let's dive into a cool math problem where we figure out the total distance Mariela needs to travel. This is a fun one, so stick around and we'll solve it together step by step. Understanding the concepts of fractions and basic algebra can help us to tackle this problem effectively. So, are you ready to put on your math hats and get started?

Understanding the Problem

In this math problem, Mariela’s journey is a key focus. Mariela has already covered a significant portion of her journey, specifically 240 meters. However, she still has a bit more to go. The problem states that the remaining distance is one-third (or the third part) of the total journey. Our mission, should we choose to accept it, is to determine the total length of Mariela's trip. To solve this, we need to combine the distance Mariela has already traveled with the remaining distance, which is represented as a fraction of the total distance. We'll use some basic algebra to set up an equation and find our answer. Make sure you're clear on what we know (the 240 meters) and what we need to find (the total distance). This understanding is crucial for setting up the problem correctly and avoiding any confusion along the way. Now, let’s get our thinking caps on and figure out how to set up the equation!

Setting Up the Equation

Okay, so let’s break down how to set up the equation for this problem, step by step, just like building with LEGOs. First things first, we need a variable, a placeholder for the unknown total distance. Let's call this total distance "x" – simple enough, right? Now, think of it like this: Mariela has traveled 240 meters, and she still has one-third of the total distance left to go. We can write "one-third of x" as (1/3)x. So, the total distance "x" can be expressed as the sum of the distance she has already covered (240 meters) and the remaining distance, which is (1/3)x. Putting it all together, our equation looks like this: x = 240 + (1/3)x. See? It’s like piecing together a puzzle! This equation tells us that the entire journey (x) is equal to 240 meters plus one-third of the journey. Now that we have our equation set up, the next step is to solve for "x." We’ll do this by isolating "x" on one side of the equation. Ready to move on to the next part? Let’s go!

Solving for 'x'

Alright, let’s get into the nitty-gritty of solving for 'x' in our equation: x = 240 + (1/3)x. The goal here is to isolate 'x' on one side of the equation so we can find out what it equals. Think of it like untangling a knot, but with math! First, we want to get all the 'x' terms on the same side. We can do this by subtracting (1/3)x from both sides of the equation. This gives us: x - (1/3)x = 240. Now, let’s simplify the left side. Subtracting (1/3)x from x is the same as subtracting one-third from one whole, which leaves us with two-thirds. So, we have (2/3)x = 240. We're getting closer! To solve for 'x', we need to get rid of the (2/3) coefficient. We can do this by multiplying both sides of the equation by the reciprocal of (2/3), which is (3/2). This gives us: (3/2) * (2/3)x = 240 * (3/2). The (3/2) and (2/3) on the left side cancel each other out, leaving us with just 'x'. On the right side, we have 240 * (3/2). To solve this, we can first multiply 240 by 3, which gives us 720. Then, we divide 720 by 2, which equals 360. So, our final answer is x = 360. That means the total distance of Mariela's journey is 360 meters. High five! You've just solved a tricky algebraic equation. Let’s take a moment to double-check our work to make sure everything adds up correctly.

Verifying the Solution

Okay, let's make sure we got this right! Verifying the solution is like the final check on a puzzle to see if all the pieces fit perfectly. We found that the total distance, 'x', is 360 meters. The problem told us Mariela traveled 240 meters, and the remaining distance is one-third of the total. So, let's calculate one-third of 360 meters: (1/3) * 360 = 120 meters. Now, if we add the distance Mariela traveled (240 meters) to the remaining distance (120 meters), we should get the total distance (360 meters). Let’s do it: 240 + 120 = 360 meters. Bingo! Our calculation checks out. This confirms that our solution, x = 360 meters, is correct. Verifying our solution not only gives us confidence in our answer but also reinforces the problem-solving process. It's always a good idea to double-check your work, especially in math. Now that we’ve verified our solution, let’s wrap up and see what we’ve learned from this problem.

Final Answer

So, guys, after all that awesome math-solving, we’ve arrived at the final answer! We figured out that the total distance of Mariela's journey is a whopping 360 meters. How cool is that? We started with a bit of a tricky problem, setting up an equation with unknowns and fractions, and then we broke it down step by step. We defined our variable, set up the equation, solved for 'x', and even verified our answer to make sure everything was spot on. Remember, in these types of problems, the key is to understand the relationships between the different parts of the journey. Mariela had already traveled 240 meters, and the remaining distance was one-third of the total. By turning this information into an equation, we were able to find the total distance. This problem wasn’t just about getting the right number; it was about understanding how math concepts like fractions and algebra can help us solve real-world situations. Whether you’re planning a trip, measuring distances, or just flexing your brain muscles, these skills are super useful. Great job sticking with it and solving this problem! Now you’ve got another tool in your math toolkit. Keep practicing, and you’ll be a math whiz in no time!

Therefore, the total distance of the journey is 360 meters.