Mateus's Journey Calculating The Shortest Distance To School

Mateus is at his house (A) and needs to go to school (B), but first he needs to go to the bank (E). The distance between A and E is 2 km, and the distance between E and B is 3 km. What is the shortest total distance Mateus has to travel to get to school?

Introduction

In this mathematical journey, we follow Mateus as he embarks on a trip from his home (A) to school (B), with a crucial stop at the bank (E) along the way. This classic problem allows us to explore the concepts of distance, optimization, and efficient route planning. We aim to determine the shortest total distance Mateus must travel to reach his school, given the distances between his home and the bank, and between the bank and the school. This scenario provides a practical application of fundamental mathematical principles, which are relevant in everyday life, such as planning errands, navigating routes, and minimizing travel time and costs. By solving this problem, we will not only find the numerical answer but also understand the reasoning behind choosing the most efficient path. This type of problem-solving skill is essential for various aspects of life, from time management to logistics and even strategic decision-making. Let's dive into the details and figure out the optimal route for Mateus!

Problem Statement: Mateus's Trip to School

Mateus is at his house (location A) and needs to go to school (location B). However, before heading to school, he must make a stop at the bank (location E). The distance between Mateus's house (A) and the bank (E) is 2 kilometers, and the distance between the bank (E) and the school (B) is 3 kilometers. The question is: what is the shortest total distance Mateus must travel to reach the school? This is a classic problem of distance optimization, where we need to find the most efficient route that minimizes the total travel distance. Understanding the layout of the locations is crucial. Mateus starts at his house (A), goes to the bank (E), and then proceeds to the school (B). The distances between these points are given: A to E is 2 km, and E to B is 3 km. The key to solving this problem is to recognize that the shortest distance between two points is a straight line. However, since Mateus has a mandatory stop at the bank, his journey will consist of two segments: the distance from his house to the bank and the distance from the bank to the school. To find the shortest total distance, we simply need to add these two distances together. This problem highlights the importance of breaking down a complex journey into smaller, manageable segments and then applying basic mathematical principles to find the optimal solution. Let's move on to the solution and calculate the shortest distance Mateus must travel.

Solution: Calculating the Shortest Distance

To find the shortest total distance Mateus must travel, we need to add the distance from his house (A) to the bank (E) and the distance from the bank (E) to the school (B). We are given that the distance between A and E is 2 kilometers, and the distance between E and B is 3 kilometers. Therefore, the calculation is straightforward: Total distance = Distance (A to E) + Distance (E to B). Substituting the given values, we get: Total distance = 2 km + 3 km. Adding these distances together, we find that the total distance is 5 kilometers. This means that the shortest route for Mateus to take, which includes a stop at the bank, is 5 kilometers. This solution assumes that the locations A, E, and B are in a straight line or form a triangle, and Mateus travels along the direct paths between these points. In real-world scenarios, the actual distance might be slightly longer due to road networks and other constraints. However, for this problem, we consider the direct distances between the locations. The solution demonstrates a simple yet crucial concept in distance calculation: adding individual segments of a journey to find the total distance. This principle is widely applicable in various fields, such as logistics, transportation, and even everyday planning. Let's summarize our findings and provide a clear answer to the problem.

Conclusion: The Shortest Route for Mateus

In conclusion, the shortest total distance Mateus must travel to reach the school, with a stop at the bank, is 5 kilometers. This was determined by adding the distance between his house and the bank (2 km) to the distance between the bank and the school (3 km). This problem illustrates a fundamental principle of distance calculation: the total distance of a journey with multiple stops is the sum of the distances of each segment. This simple yet powerful concept is applicable in numerous real-world situations, from planning daily commutes to optimizing delivery routes. Understanding how to calculate the shortest distance is crucial for efficient travel and time management. In Mateus's case, taking the direct route from his house to the bank and then to the school ensures he travels the minimum possible distance. This problem also highlights the importance of clear problem-solving skills. By breaking down the problem into smaller parts and applying basic mathematical principles, we were able to arrive at the correct solution. Effective problem-solving is a valuable skill in mathematics and beyond, enabling us to tackle complex challenges with confidence and precision. We hope this explanation provides a clear understanding of how to calculate the shortest distance for Mateus's journey. This exercise not only solves a specific problem but also reinforces the importance of mathematical reasoning in everyday life.

Further Exploration

To further explore the concepts of distance and optimization, we can consider several extensions of this problem. One interesting variation would be to introduce different routes or paths between the locations and ask which route is the shortest. For example, if there were an alternate route from Mateus's house to the school that bypassed the bank but was a longer distance, we could compare the total distances of both routes to determine the most efficient option. Another extension could involve adding time constraints. Suppose Mateus has a limited amount of time to reach school and each segment of the journey has a different speed limit. In this case, we would need to consider not only the distance but also the time taken for each segment to find the quickest route. We could also explore scenarios with multiple stops. Imagine Mateus needs to visit several locations before going to school. This would require calculating the distances between all the locations and finding the optimal order of visits to minimize the total travel distance. These types of problems often involve more complex mathematical techniques, such as graph theory and optimization algorithms. Furthermore, we can relate this problem to real-world applications like route planning for delivery services or navigation systems. These systems use algorithms to find the shortest or fastest routes between multiple destinations, taking into account factors like traffic, road closures, and other constraints. By exploring these extensions and real-world applications, we can gain a deeper appreciation for the practical relevance of distance and optimization concepts.

Keywords: distance, optimization, shortest route, mathematical problem, problem-solving, route planning, travel distance, efficiency, total distance, real-world applications