Calculate Thuto's Running Time For 10 Km

Hey guys! Let's dive into a classic math problem: Thuto runs 6 km in 24 minutes. The big question is: How long will it take him to run 10 km, assuming he keeps up that same steady speed? This is a great example of a proportionality problem, and we'll break it down step by step to make sure we nail it. Understanding how to solve these kinds of problems is super useful, not just for math class, but also in real life. You know, figuring out travel times, scaling recipes, or even estimating how long a project will take. So, let's get started and make sure we all understand how to find the answer. We'll examine the information, find the secret to solve it and do all the calculations. You got this!

Understanding the Problem: Speed, Distance, and Time

Alright, first things first, let's make sure we totally get what the problem is asking. We're given a few key pieces of information. Firstly, Thuto's distance and time, we know he runs 6 km in 24 minutes. This initial info is crucial because it gives us Thuto's speed. Then, the real question: We need to figure out how long it will take him to run 10 km. This is the ultimate goal. The trick to solving this problem lies in knowing that Thuto's speed is constant. This means he covers the same distance in the same amount of time. It's like he's on cruise control. Constant speed is the key.

To solve this, we'll use the fundamental relationship between speed, distance, and time. This relationship can be expressed as: Speed = Distance / Time. Or, you can rearrange it to find time: Time = Distance / Speed. To start, we're going to calculate Thuto's speed from the information provided. Once we know his speed, we can calculate the time it takes him to run 10 km. Remember, the key is using the right formula and keeping track of units. Let's make sure we're consistent with our units. If the distance is in kilometers, and time is in minutes, our speed will be in kilometers per minute. This will help us later. Now that we have a solid understanding of the problem and the tools we need, let's get to work!

Step-by-Step Solution: Finding the Answer

Okay, guys, time to roll up our sleeves and solve this problem! We will use the approach and break it down into easy-to-follow steps. First things first, we must find Thuto's speed. We know he runs 6 km in 24 minutes. Using the formula Speed = Distance / Time, we can calculate his speed. So, Speed = 6 km / 24 minutes = 0.25 km/minute. Awesome! Now we know Thuto runs 0.25 kilometers every minute. Now that we know his speed, we can calculate how long it takes him to run 10 km. We use the formula Time = Distance / Speed. Therefore, Time = 10 km / 0.25 km/minute = 40 minutes. So, it will take Thuto 40 minutes to run 10 km. But wait a minute! The answer options are in hours. We need to convert 40 minutes into hours. Remember, there are 60 minutes in an hour. To convert minutes to hours, we divide the number of minutes by 60. So, 40 minutes / 60 minutes/hour = 2/3 hours. Bada bing, bada boom, we've got our answer! Always double-check your work, guys. Make sure you've used the correct formulas, and your units are consistent. Now, let's see which of the options matches our answer.

Checking the Answer Choices and Final Answer

Alright, we've done the heavy lifting, now it's time to check our answer against the multiple-choice options. Our calculated time for Thuto to run 10 km is 40 minutes, which we converted into 2/3 of an hour. Let's look at the options:

A. $\frac{1}{4}$ hour: This is equivalent to 15 minutes, definitely not our answer. B. $\frac{2}{5}$ hour: This is equivalent to 24 minutes, again, not our answer. C. $\frac{2}{3}$ hour: This is equivalent to 40 minutes, which perfectly matches our calculation! This is most likely our correct answer. D. $\frac{5}{2}$ hour: This is equivalent to 150 minutes, which is way off.

So, by carefully comparing our result with the options, it's clear that the correct answer is C. $\frac{2}{3}$ hour. Hooray, we did it! We have successfully solved the problem. The process involved understanding the relationship between distance, speed, and time. We then used this knowledge to calculate Thuto's speed and, finally, determine how long it would take him to run 10 km. Always remember to break down complex problems into smaller, manageable steps. This will make the process easier and prevent any mistakes. Also, double-checking your work and converting your units when needed is essential. High five, guys!

Further Practice and Resources

Want to become a speed-running expert? Here are some ways to keep your math skills sharp, guys: Practice, practice, practice! The more you work through problems like this, the better you'll get. Try changing the distances and times to make new problems. For example, what if Thuto ran 8 km in 30 minutes? Or, what if he wanted to run 15 km? Create your own problems and solve them. This will help you understand the concepts more deeply.

• Online Resources: There are tons of online resources to help you, such as Khan Academy. They offer tons of free math lessons and practice exercises. Use them! There are also tons of fun math games. They can make learning more engaging. Who said math couldn't be fun, right? Try searching for "speed, distance, and time" problems or "proportionality problems." You'll find tons of examples. Also, check out educational YouTube channels. Many of them offer clear explanations and worked examples. Watching videos can be a great way to understand the concepts. It can also help you see different ways to approach the problem.

• Textbooks and Workbooks: Don't underestimate the power of a good old-fashioned textbook or workbook. They often have practice problems and answer keys. This is great for checking your work and identifying areas where you need more practice.

• Study Groups: Studying with friends can be beneficial. You can discuss problems, help each other, and learn from each other's mistakes. This is a great way to review, too. Remember, the goal is to practice regularly and stay consistent. Keep practicing and keep up the great work, you are doing great! Now, go out there, be confident, and start solving math problems. You can do it!