Distance-Time Problem: Car Traveling 180 Km In 3 Hours
Hey guys! Let's dive into this interesting math problem. We're tackling a question about distance, time, and speed. It seems like we need to figure out how far a car travels in a specific time frame, given some initial information. So, let's break it down step by step and make sure we understand the concepts involved. This isn't just about finding the right answer; it's about understanding why the answer is correct. Think of it as building a solid foundation for more complex problems later on. Ready to get started? Let’s jump right in!
Understanding the Problem
Okay, so the core of this problem revolves around the relationship between distance, time, and speed. These three are like the main characters in our little mathematical story. The problem gives us a scenario: A car travels 180 kilometers in 3 hours. Our mission, should we choose to accept it (and we do!), is to find out how many kilometers the car will travel in 2 hours, assuming it maintains a consistent speed. This is a classic example of a direct proportion problem. What does that mean? Well, it means that if we decrease the time, the distance traveled will also decrease proportionally. Think about it: If you drive for less time, you're going to cover less ground, right? The key here is that the speed remains constant. If the car suddenly sped up or slowed down, things would get a lot more complicated! So, to solve this, we need to figure out the car's speed first. Once we know how many kilometers the car covers in one hour, we can easily calculate the distance covered in any given number of hours. It’s like finding the magic number that unlocks the rest of the problem. We'll use this speed to then find the distance traveled in 2 hours. This is where our mathematical toolkit comes into play – specifically, the formula that connects distance, time, and speed. We’re not just pulling numbers out of thin air; we're using a fundamental principle of physics to guide our calculations. This approach ensures we not only get the right answer but also understand the underlying logic, which is super important for tackling similar problems in the future. So, let's roll up our sleeves and get calculating!
Calculating the Speed
Alright, so we know the car travels 180 kilometers in 3 hours. To find the car's speed, we need to figure out how many kilometers it travels in one hour. This is where the concept of speed as a rate comes into play. Speed is essentially the rate at which distance is covered over time. Think of it like this: if you're running, your speed tells you how many meters you cover each second. In this case, we want to find the kilometers covered each hour. The formula we're going to use is quite simple, but incredibly powerful: Speed = Distance / Time. This formula is the key to unlocking our problem. It's like a secret code that translates distance and time into speed. Now, let's plug in the values we know. The distance is 180 kilometers, and the time is 3 hours. So, our equation looks like this: Speed = 180 km / 3 hours. Doing the division, we get Speed = 60 kilometers per hour (km/h). This is a crucial piece of information. We now know that the car is traveling at a steady 60 kilometers every hour. This is our magic number! It allows us to predict how far the car will travel in any given amount of time, as long as it maintains this speed. Understanding this step is super important because it’s not just about getting a number; it’s about grasping the relationship between distance, time, and speed. We've essentially broken down the problem into smaller, more manageable parts. We’ve found the speed, which is the constant factor in this scenario. Now, we can use this speed to calculate the distance traveled in 2 hours, which is the final piece of the puzzle. Let’s move on to the next step and put this speed to work!
Determining the Distance in 2 Hours
Now that we've successfully calculated the car's speed – a steady 60 kilometers per hour – we're ready to tackle the final part of the problem: figuring out how far the car travels in 2 hours. We already know the fundamental relationship between distance, speed, and time: Distance = Speed × Time. This formula is like the reverse of the one we used earlier to find the speed. It’s essentially the same relationship, just rearranged to help us find a different variable. We've already got the speed (60 km/h), and we're given the time (2 hours). So, all that's left to do is plug these values into the formula and do the multiplication. Let's set up the equation: Distance = 60 km/h × 2 hours. When we multiply 60 by 2, we get 120. So, the distance the car travels in 2 hours is 120 kilometers. And that's it! We've solved the problem. But let's not stop here. It's always a good idea to take a moment and think about whether our answer makes sense in the context of the problem. We know the car travels 180 kilometers in 3 hours. Since 2 hours is less than 3 hours, we would expect the distance traveled in 2 hours to be less than 180 kilometers. Our answer of 120 kilometers fits that expectation. This kind of sanity check is a valuable tool for catching potential errors. It's like having a built-in error detector that helps us ensure our calculations are on the right track. We’ve not only found the answer but also validated it, which gives us extra confidence in our solution. Now, let's take a look at the answer choices provided in the problem and see which one matches our calculated distance.
Matching the Answer
Okay, we've done the math and figured out that the car travels 120 kilometers in 2 hours. Now, let's take a look at the answer choices given in the problem and see if we can find a match. The options are:
A) 130 km B) 120 km C) 140 km D) 150 km
Looking at these options, it's pretty clear that option B) 120 km matches our calculated distance exactly. This is great! It confirms that we've followed the correct steps and arrived at the right answer. But why is it so important to have these multiple-choice options? Well, they serve a couple of purposes. First, they give us a set of potential answers to choose from, which can be helpful in guiding our thinking. If we had made a mistake in our calculations and ended up with a number that wasn't on the list, it would be a red flag telling us to go back and check our work. Second, multiple-choice questions often include distractors – answers that seem plausible but are actually incorrect. These distractors can test our understanding of the concepts and our ability to apply them correctly. In this case, the other options (130 km, 140 km, and 150 km) might seem reasonable at first glance, but they don't fit the mathematical relationship between distance, speed, and time that we've established. So, by carefully working through the problem and understanding the underlying principles, we've been able to confidently select the correct answer. It’s like having a roadmap that guides us through the problem and helps us avoid common pitfalls. With that, we can confidently say that we've solved the problem completely! We’ve understood the question, performed the necessary calculations, and matched our answer with the correct option. Nice work!
Final Answer
Alright, let's wrap things up! We've journeyed through the problem step-by-step, and now we're at the final destination: the answer. After carefully analyzing the problem, calculating the car's speed, and then determining the distance it travels in 2 hours, we arrived at the answer of 120 kilometers. We then matched this result with the multiple-choice options provided and found that B) 120 km is the correct answer. This entire process highlights the importance of breaking down a problem into smaller, manageable steps. We didn't just try to guess the answer; we used our knowledge of the relationship between distance, speed, and time to systematically solve the problem. This approach not only helps us find the right answer but also builds our problem-solving skills for future challenges. Think of it as building a toolbox filled with different strategies and techniques that we can use to tackle all sorts of mathematical puzzles. So, the final answer is definitively B) 120 km. We've not only found the solution, but we've also understood the process and validated our answer. This is the ultimate goal – not just getting the answer right, but understanding why it's right. And with that, we've conquered this distance-time problem! You guys did awesome following along. Keep practicing and breaking down problems, and you'll become math problem-solving pros in no time!
