Tourist Route Calculation: Find The Total Distance

Hey guys! Ever wondered how to calculate the total distance of a tourist route when you only know the fractions covered on different days? Let's dive into a fun math problem where we figure out just that! This is a classic problem often encountered in mathematics, and understanding it can help you solve similar real-world scenarios. So, let’s break it down step by step and make it super easy to understand.

Understanding the Problem

First, let’s make sure we understand the problem clearly. In this scenario, a tourist travels a fraction of the total route on the first day and another fraction on the second day. We know the exact distance covered in these two days combined. The challenge? To find the total length of the entire tourist route. This involves a bit of fraction arithmetic and some basic algebraic thinking. Don’t worry, we’ll go through it together!

Key Information to Note:

• The fraction of the route traveled on the first day.
• The fraction of the route traveled on the second day.
• The total distance covered in the two days.

Our goal is to find the total distance of the route. To do this effectively, we will use a combination of fraction addition and solving a simple equation. Let's get started!

Setting Up the Equation

Alright, let's get to the heart of the problem and set up the equation. This is where we translate the word problem into mathematical language. This might sound intimidating, but it’s actually quite straightforward once you get the hang of it. We’ll use a variable to represent the unknown – in this case, the total distance of the tourist route.

Let's use 'x' to represent the total distance of the route in kilometers. According to the problem, the tourist traveled a certain fraction of 'x' on the first day and another fraction of 'x' on the second day. The sum of these distances is equal to the total distance traveled in the two days, which we know is 36 km. So, we can write the equation like this:

(Fraction traveled on the first day) * x + (Fraction traveled on the second day) * x = 36

Now, let’s replace "Fraction traveled on the first day" and "Fraction traveled on the second day" with the actual fractions given in the problem. If the tourist traveled 1/4 of the route on the first day and 1/7 of the route on the second day, the equation becomes:

(1/4) * x + (1/7) * x = 36

This equation is the key to solving our problem. It tells us that the sum of the distances traveled on the first and second days equals 36 km. Now, let's move on to solving this equation.

Solving the Equation

Okay, guys, we've set up the equation, and now it's time to roll up our sleeves and solve it! Solving the equation involves a few steps, but don't worry, we'll take it nice and slow. The main goal here is to isolate 'x' on one side of the equation, which will give us the value of the total distance.

Our equation is:

(1/4) * x + (1/7) * x = 36

The first step is to combine the terms with 'x'. To do this, we need to find a common denominator for the fractions 1/4 and 1/7. The least common multiple (LCM) of 4 and 7 is 28, so we'll convert both fractions to have this denominator. This gives us:

(7/28) * x + (4/28) * x = 36

Now, we can add the fractions:

(7/28 + 4/28) * x = 36

(11/28) * x = 36

Next, to isolate 'x', we need to get rid of the fraction 11/28. We can do this by multiplying both sides of the equation by the reciprocal of 11/28, which is 28/11. This gives us:

x = 36 * (28/11)

Now, we perform the multiplication:

x = (36 * 28) / 11

x = 1008 / 11

Finally, we divide 1008 by 11 to find the value of 'x'.

Calculating the Final Answer

Alright, let's crunch the numbers and find our final answer! We've reached the last step in our journey to solve this math problem. We have the equation:

x = 1008 / 11

Now, we just need to perform the division. When we divide 1008 by 11, we get:

x ≈ 91.64

So, the total distance of the tourist route is approximately 91.64 kilometers. However, in practical terms, we might want to round this to a more sensible number, depending on the context of the problem. For instance, if we need a whole number, we might round it to 92 kilometers.

Practical Application and Conclusion

Guys, we did it! We successfully calculated the total distance of the tourist route. This wasn't just an abstract math problem; it's something that has practical applications in real-life scenarios. Understanding how to work with fractions and solve equations can help you in various situations, from planning trips to managing budgets.

Why is this important?

• Trip Planning: Knowing how to calculate distances is essential when planning a trip. You can estimate travel times, fuel costs, and more accurately plan your itinerary.
• Budgeting: If you need to allocate a budget for different parts of a project or journey, understanding fractions and proportions can be incredibly useful.
• Everyday Problem Solving: These skills are valuable in many everyday situations, from cooking to home improvement projects.

In conclusion, the ability to break down a problem, set up an equation, and solve it is a powerful tool. Math isn’t just about numbers; it’s about thinking logically and solving problems effectively. So, the next time you encounter a similar problem, you’ll be well-equipped to tackle it! Keep practicing, and math will become your superpower!