Graphing Distance Vs. Time: Rustam's Bike Ride At 15 Km/h

Hey guys! Let's dive into a fun math problem involving Rustam and his bike ride. He's cruising at a steady speed, and we're going to graph his journey and make a table to track his progress. This is a classic example of how math can help us understand the world around us, especially when it comes to movement and speed.

Understanding the Problem: Rustam's Constant Speed

So, the core of this problem is that Rustam is riding his bike at a constant speed of 15 km/h. This “constant speed” part is super important because it means his speed isn't changing – he's not speeding up or slowing down. This makes our calculations much simpler. Think of it like setting your car's cruise control – the speed stays the same. To effectively graph Rustam's journey and build a table of values, we need to grasp the relationship between distance, time, and speed. The fundamental formula that connects these three is: distance = speed × time. This formula is the key to unlocking the problem. We know Rustam's speed (15 km/h), and we'll be given different time values. By plugging these values into the formula, we can find the corresponding distances he travels. This will give us the data points we need to plot the graph and fill in our table. This concept isn't just limited to bike rides; it applies to various real-world scenarios involving constant motion, such as cars on the highway, airplanes in flight, or even the movement of celestial bodies. Grasping this relationship empowers us to make predictions and analyze motion in countless situations. So, with our constant speed in mind, let's move on to graphing Rustam's journey, visualizing his progress as time passes.

Creating the Graph: Visualizing Rustam's Journey

Alright, let's get visual! We're going to plot a graph to show how far Rustam travels over time. This graph will be our visual representation of his journey. Now, when we're making a graph of distance versus time, we always put time on the horizontal axis (also called the x-axis) and distance on the vertical axis (or y-axis). Think of it like this: time is marching forward, and as it does, Rustam covers more distance. Each point on our graph will represent a specific moment in time and the corresponding distance Rustam has traveled at that moment. To draw the graph, we first need some points. Remember the formula: distance = speed × time? We know Rustam's speed is 15 km/h, so we can use this formula to calculate the distances for different times. For example, after 1 hour, he would have traveled 15 km (15 km/h × 1 h = 15 km). After 2 hours, he'd have traveled 30 km, and so on. We can calculate a few more points to get a good idea of the graph's shape. Now, here's the cool part: since Rustam's speed is constant, the graph will be a straight line. This is because the distance increases steadily with time. If he sped up or slowed down, the line would curve, but because he's maintaining a constant pace, we get a nice, straight line. To draw the line, we just need to plot two points and connect them with a ruler. It's that simple! The steeper the line, the faster Rustam is going. A flatter line would mean he's traveling slower. Our graph is a powerful tool for visualizing Rustam's journey, showing us at a glance how far he travels over any given period. Now, let's move on to creating a table of values, which will give us specific data points to analyze his progress even further.

Building the Table: Time and Distance Values

Now, let's get organized and create a table that shows the exact distances Rustam has traveled at specific times. This table will complement our graph, giving us precise data points to analyze his journey. So, a table like this is just a way of organizing information into rows and columns. In our case, one column will represent time (in hours), and the other column will represent the corresponding distance Rustam has traveled (in kilometers). We're given some specific times to consider: 1/5 hour, 1/4 hour, 1/3 hour, and 1/2 hour. These are fractions of an hour, so we'll need to do a little math to figure out the distances. Remember our trusty formula: distance = speed × time. Rustam's speed is 15 km/h, so we'll use that in our calculations. Let's take the first time, 1/5 hour. To find the distance, we multiply 15 km/h by 1/5 hour: 15 × (1/5) = 3 km. So, after 1/5 of an hour, Rustam has traveled 3 kilometers. We'll do the same calculation for the other times. For 1/4 hour: 15 × (1/4) = 3.75 km. For 1/3 hour: 15 × (1/3) = 5 km. And finally, for 1/2 hour: 15 × (1/2) = 7.5 km. Now we have all the data points we need to fill in our table. Each row will represent a specific time, and the corresponding distance will be in the next column. This table is super useful because it gives us a quick reference for Rustam's location at any of these times. We can see exactly how far he's gone without having to look at the graph. The table and the graph work together to give us a complete picture of Rustam's bike ride. The graph gives us a visual overview, while the table provides the precise data. Next, let’s summarize everything we've learned about Rustam's journey!

Here’s the completed table:

Putting It All Together: Rustam's Bike Ride Recap

Okay, guys, let's recap what we've learned about Rustam's bike ride! We started with the key piece of information: Rustam is riding at a constant speed of 15 km/h. This is crucial because it makes the relationship between distance, time, and speed straightforward. We used the formula distance = speed × time to understand how these three are connected. First, we created a graph to visualize his journey. We plotted time on the horizontal axis and distance on the vertical axis. Since his speed is constant, the graph is a straight line, which makes it easy to see how the distance increases steadily over time. A steeper line would indicate a higher speed, while a flatter line would mean a lower speed. The graph gives us a great visual overview of Rustam's progress. Then, we built a table of values. This table showed us the exact distances Rustam traveled at specific times: 1/5 hour, 1/4 hour, 1/3 hour, and 1/2 hour. We used the same formula (distance = speed × time) to calculate these distances. The table provides precise data points, complementing the visual representation of the graph. Together, the graph and the table give us a complete picture of Rustam's bike ride. The graph allows us to see the overall trend, while the table provides the specific details. This exercise demonstrates how math can be used to model real-world situations, such as motion at a constant speed. By understanding the relationships between distance, time, and speed, we can make predictions and analyze various scenarios. So, next time you see someone riding a bike, remember Rustam and his constant speed – and how we can use math to track his journey!