Calculating Average Speed A Cyclist's Journey Over 150 Km

Hey guys! Ever wondered how to calculate the average speed of a cyclist covering a long distance? Let's break down a fun math problem together! We're going to explore a scenario where a cyclist travels 150 km over 4 days, spending 3 hours each day pedaling away. Our mission? To find out the average speed they maintained throughout this journey. So, grab your imaginary helmets, and let's dive into the world of speed, distance, and time!

Understanding the Problem

Okay, so here’s the deal. A cyclist rides a total of 150 km over a span of 4 days. Each day, they're clocking in 3 hours on the bike. The big question is: what was their average speed during the entire trip? To solve this, we need to understand the relationship between distance, time, and speed. Remember that classic formula? Speed = Distance / Time. This is our golden ticket to cracking this problem. But before we jump into the calculations, let’s make sure we've got all our ducks in a row. We know the total distance, but what about the total time? That's our next little puzzle piece.

Total Time Calculation

First things first, we need to figure out the total time the cyclist spent pedaling. They rode for 3 hours each day, and this went on for 4 days. So, how do we find the total hours? Simple! We multiply the number of hours per day by the number of days. This means we're doing 3 hours/day * 4 days. Doing the math, 3 multiplied by 4 gives us 12 hours. So, the cyclist spent a total of 12 hours on their bike over the 4 days. Now that we have the total time, we're one step closer to finding the average speed. It's like we're detectives solving a mystery, and each calculation is a new clue that brings us closer to the solution. With the total distance and total time in hand, we're ready to roll into the final calculation!

Applying the Formula: Speed = Distance / Time

Alright, let's get down to the nitty-gritty! We've got our formula ready: Speed = Distance / Time. We know the total distance is 150 km, and we've calculated the total time to be 12 hours. Now it's just a matter of plugging these numbers into our formula. So, we have Speed = 150 km / 12 hours. When we perform this division, we're essentially figuring out how many kilometers the cyclist covered in each hour, on average. Think of it like slicing up the total distance into equal parts, one for each hour of the ride. Now, let's do the division. 150 divided by 12 gives us 12.5. This means the cyclist traveled 12.5 kilometers in each hour, on average. And that, my friends, is our average speed! We've successfully navigated through the problem and found our answer. But before we celebrate, let's just double-check everything to make sure we're spot on.

Verifying the Result

Okay, before we proudly declare our victory, let’s quickly verify our result. We found that the cyclist's average speed was 12.5 km/h. A good way to check this is to reverse the calculation. If we multiply the average speed by the total time, we should get the total distance. So, let's try it out: 12. 5 km/h * 12 hours. When we multiply these numbers, we get 150 km. Ta-da! This matches our original total distance, which means our calculation is correct. It's always a good practice to double-check your work, especially in math problems. This way, you can be super confident in your answer. Now that we've verified our result, we can confidently say that the cyclist's average speed was indeed 12.5 km/h. We've tackled the problem, solved it, and even double-checked it. High-five for being awesome problem-solvers!

Identifying the Correct Option

Now that we've done the math and found the average speed, let's circle back to the options given in the problem. We had four choices: A) 10 km/h, B) 12.5 km/h, C) 15 km/h, and D) 20 km/h. Remember our calculation? We found the average speed to be 12.5 km/h. Looking at the options, we can clearly see that option B matches our result. So, the correct answer is B) 12.5 km/h. This is like finding the treasure after following the map – we knew what we were looking for, and we successfully found it! Identifying the correct option is the final step in solving the problem, and it feels great to get it right. Now, let's wrap things up with a quick recap of what we've learned.

Conclusion: Average Speed Calculation

Alright, guys, let's wrap things up! We've journeyed through a fun problem involving a cyclist's adventure, and we've learned how to calculate average speed. We started with a cyclist traveling 150 km over 4 days, pedaling 3 hours each day. Our mission was to find the average speed maintained during this trip. We broke down the problem step by step: first, we calculated the total time by multiplying the hours per day by the number of days, giving us 12 hours. Then, we applied the formula Speed = Distance / Time, plugging in our values to get Speed = 150 km / 12 hours. This gave us an average speed of 12.5 km/h. We even verified our result to make sure we were spot on. Finally, we identified the correct option from the choices provided, which was B) 12. 5 km/h.

This problem is a fantastic example of how math can be applied to real-life situations. Understanding the relationship between distance, time, and speed is not just useful for solving math problems; it's also helpful in understanding everyday scenarios, like planning a trip or estimating travel time. So, the next time you're thinking about speed and distance, remember this cyclist's journey, and you'll have a solid foundation to work with. Keep practicing, keep exploring, and most importantly, keep enjoying the world of math! You've got this!

Final Answer

The final answer is B) 12,5 km/h.