Calculating the Total Route Distance

Oct 13, 2025 by wbrum.org 102 views

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Introduction

Cycling tours are a popular way to explore new places and enjoy the great outdoors. However, navigating the route and calculating the total distance can be a daunting task, especially for beginners. In this article, we will explore a scenario where a group of cyclists traveled a certain distance in the first two hours and a fixed distance in the third hour. We will use mathematical concepts to calculate the total route distance.

Understanding the Problem

Let's break down the problem statement:

The participants traveled 1/4 of Percuso in the first hour.
They traveled 2/5 of Percuso in the second hour.
In the third and last hour, they traveled 14 kilometers.

We are asked to find the total route distance of the tour.

Calculating the Total Route Distance

To calculate the total route distance, we need to find the distance traveled in the first two hours and add it to the distance traveled in the third hour.

Distance Traveled in the First Hour

The participants traveled 1/4 of Percuso in the first hour. Let's assume Percuso is a certain distance, say x kilometers. Then, the distance traveled in the first hour is:

1/4 * x = x/4 kilometers

Distance Traveled in the Second Hour

The participants traveled 2/5 of Percuso in the second hour. Using the same assumption as before, the distance traveled in the second hour is:

2/5 * x = 2x/5 kilometers

Distance Traveled in the Third Hour

The participants traveled 14 kilometers in the third hour.

Total Route Distance

To find the total route distance, we need to add the distances traveled in the first two hours and the distance traveled in the third hour:

Total Route Distance = (x/4) + (2x/5) + 14

Simplifying the Expression

To simplify the expression, we need to find a common denominator. The least common multiple of 4 and 5 is 20. So, we can rewrite the expression as:

Total Route Distance = (5x/20) + (8x/20) + 14

Combine like terms:

Total Route Distance = (13x/20) + 14

Finding the Value of x

We are given that the total route distance is equal to the sum of the distances traveled in each hour. Let's call the total route distance y kilometers. Then, we can set up the equation:

y = (13x/20) + 14

We are also given that the participants traveled 14 kilometers in the third hour. This means that the total route distance is at least 14 kilometers. So, we can set up the inequality:

y ≥ 14

Solving the Inequality

To solve the inequality, we need to isolate the variable x. We can start by subtracting 14 from both sides:

y - 14 ≥ 0

Now, we can substitute the expression for y:

(13x/20) + 14 - 14 ≥ 0

Simplify the expression:

(13x/20) ≥ 0

Multiply both sides by 20:

13x ≥ 0

Divide both sides by 13:

x ≥ 0

Finding the Value of x

We know that x is a distance, and distances cannot be negative. So, we can conclude that x ≥ 0.

Finding the Total Route Distance

Now that we have found the value of x, we can substitute it into the expression for the total route distance:

Total Route Distance = (13x/20) + 14

Substitute x = 0:

Total Route Distance = (13(0)/20) + 14

Simplify the expression:

Total Route Distance = 0 + 14

Total Route Distance = 14

Conclusion

In this article, we calculated the total route distance of a cycling tour. We used mathematical concepts to find the distance traveled in each hour and added them together to find the total route distance. We found that the total route distance is at least 14 kilometers.

Final Answer

The final answer is 14.

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Introduction

In our previous article, we explored a scenario where a group of cyclists traveled a certain distance in the first two hours and a fixed distance in the third hour. We used mathematical concepts to calculate the total route distance. In this article, we will answer some frequently asked questions related to the problem.

Q&A

Q: What is the total route distance of the tour?

A: The total route distance of the tour is at least 14 kilometers.

Q: How did you calculate the total route distance?

A: We calculated the total route distance by finding the distance traveled in each hour and adding them together. We used the formula:

Total Route Distance = (13x/20) + 14

where x is the distance traveled in the first two hours.

Q: What is the value of x?

A: We found that x ≥ 0, which means that the distance traveled in the first two hours is at least 0 kilometers.

Q: Why did you assume that Percuso is a certain distance, say x kilometers?

A: We assumed that Percuso is a certain distance, say x kilometers, to simplify the problem. This allowed us to express the distance traveled in each hour in terms of x.

Q: Can you explain the concept of a common denominator?

A: A common denominator is the least common multiple of two or more numbers. In this case, we found that the least common multiple of 4 and 5 is 20. This allowed us to rewrite the expression for the total route distance with a common denominator.

Q: How did you simplify the expression for the total route distance?

A: We simplified the expression for the total route distance by combining like terms and finding a common denominator.

Q: What is the significance of the inequality y ≥ 14?

A: The inequality y ≥ 14 represents the fact that the total route distance is at least 14 kilometers.

Q: Can you explain the concept of solving an inequality?

A: Solving an inequality involves isolating the variable and finding the solution set. In this case, we solved the inequality by subtracting 14 from both sides and then multiplying both sides by 20.

Q: What is the final answer to the problem?

A: The final answer to the problem is 14 kilometers.

Conclusion

In this article, we answered some frequently asked questions related to the problem of calculating the total route distance of a cycling tour. We used mathematical concepts to find the distance traveled in each hour and added them together to find the total route distance. We found that the total route distance is at least 14 kilometers.

Final Answer

The final answer is 14 kilometers.