Pedro's Journey: How Much Further To Walk?

Hey guys! Let's dive into a fun math problem today. We've got Pedro, who's on a long walk, and we need to figure out how much further he has to go. This kind of problem involves fractions and a bit of logical thinking, so let's break it down step by step to make it super clear.

Understanding the Problem

So, our main goal here is to figure out how many kilometers Pedro still needs to walk. To get there, we first need to understand the journey Pedro has already taken. The total distance is 48 kilometers, which is a good starting point. Pedro initially walks 3/4 of the total distance. Then, after a break, he walks an additional 1/6 of what's left. This is the key part – we need to calculate what's left after the first leg of the journey before we can figure out the second part. This problem is a classic example of how math problems can mirror real-life situations, and breaking it down into smaller, manageable parts is the key to solving it. Let's tackle the first part: how much did Pedro walk initially?

Calculating the Initial Distance Walked

Okay, so Pedro initially walked 3/4 of the 48 km path. To figure out the initial distance Pedro walked, we need to calculate what 3/4 of 48 is. In mathematical terms, this means we need to multiply 3/4 by 48. When we multiply a fraction by a whole number, we can think of the whole number as a fraction with a denominator of 1. So, we have (3/4) * (48/1). To multiply fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers). That gives us (3 * 48) / (4 * 1), which simplifies to 144/4. Now, we just need to divide 144 by 4 to get our answer. 144 divided by 4 is 36. So, Pedro walked 36 kilometers in the first part of his journey. This is a significant portion of the total distance, but we're not done yet! We need to figure out how much further Pedro walked after his rest stop. But before we do that, let’s calculate the remaining distance after the initial walk. This will help us understand the next part of the problem more clearly.

Determining the Remaining Distance

Now that we know Pedro walked 36 kilometers initially, let's figure out the distance Pedro had left to walk before he took his break. The total distance of the path is 48 kilometers, and he's already covered 36 kilometers. To find the remaining distance, we subtract the distance he walked from the total distance. So, 48 km (total) - 36 km (walked) = 12 km. This means that after walking 3/4 of the path, Pedro had 12 kilometers left to go. This is an important number because it's the base for our next calculation. Pedro didn't walk the entire remaining 12 kilometers in his second leg; he only walked 1/6 of it. So, to figure out how much he walked after his break, we need to calculate 1/6 of 12 kilometers. This is where we use the same principle of multiplying fractions that we used earlier. This step is crucial because it helps us understand how much closer Pedro got to his destination after his rest. Understanding the remaining distance helps put the problem into perspective and makes the next calculation much easier to grasp. Let’s move on to calculating the distance Pedro covered after his break.

Calculating the Distance Walked After the Break

After his break, Pedro walked 1/6 of the remaining distance. We already know that the remaining distance after the break was 12 kilometers. So, we need to calculate 1/6 of 12 km. Just like before, we can think of 12 as a fraction (12/1) and multiply the fractions: (1/6) * (12/1). Multiplying the numerators gives us 1 * 12 = 12, and multiplying the denominators gives us 6 * 1 = 6. So, we have the fraction 12/6. Now we simplify this fraction by dividing the numerator by the denominator: 12 ÷ 6 = 2. Therefore, Pedro walked 2 kilometers after his break. This is a significant piece of the puzzle. Now we know how much Pedro walked initially and how much he walked after his break. To find out how much further he still needs to walk, we need to combine this information and subtract it from the total distance. Are you still with me? Great! Let's move on to the final step – calculating the remaining distance.

Finding the Final Answer

Alright, we're in the home stretch! We know that Pedro initially walked 36 kilometers, and after his break, he walked an additional 2 kilometers. Now, to figure out the total distance Pedro walked, we simply add these two distances together: 36 km + 2 km = 38 km. So, Pedro has walked a total of 38 kilometers so far. But the question we're trying to answer is: how many kilometers does Pedro still need to walk? We know the total distance of the path is 48 kilometers. To find the remaining distance, we subtract the total distance Pedro walked from the total distance of the path: 48 km (total) - 38 km (walked) = 10 km. So, the final answer is that Pedro still needs to walk 10 kilometers. This was a multi-step problem, but we broke it down piece by piece, making it much easier to solve. Isn’t it satisfying when you can solve a challenging problem like this? Now, let's recap the steps we took to solve this problem to reinforce our understanding.

Reviewing the Steps

Let's do a quick recap of the steps to solve distance problems so we can make sure we've got it all down pat. First, we figured out the initial distance Pedro walked, which was 3/4 of 48 km, and we found that to be 36 km. Then, we calculated the remaining distance after the first leg, which was 48 km - 36 km = 12 km. Next, we determined the distance Pedro walked after his break, which was 1/6 of the remaining 12 km, and that turned out to be 2 km. Finally, we added the two distances Pedro walked (36 km + 2 km = 38 km) and subtracted that from the total distance (48 km) to find that Pedro still needs to walk 10 km. By breaking the problem into smaller, more manageable steps, we were able to tackle it effectively. This strategy is useful not just in math but in many areas of life. When faced with a complex task, breaking it down into smaller steps can make it feel less daunting and much easier to accomplish. So, guys, that’s how we solve this distance problem! Remember, the key is to read carefully, break the problem down, and take it one step at a time. Keep practicing, and you'll become math whizzes in no time!

Conclusion

So, to wrap it all up, Pedro still has 10 kilometers left to walk. We solved this problem by carefully breaking it down into manageable steps. We calculated the initial distance, then the remaining distance, then the distance walked after the break, and finally, we subtracted the total walked distance from the total distance to find the answer. Remember, math problems like these are like puzzles; each piece of information is a clue that helps you get closer to the solution. The more you practice these kinds of problems, the better you'll become at spotting the clues and putting them together. Keep challenging yourselves, and you'll find that even the toughest problems become easier with practice. Keep up the great work, guys, and I'll see you in the next math adventure!