Car Trip: Find Distance Of Hour 1

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Let's break down this distance problem step by step, guys. We're dealing with a car that travels different distances over three hours, and our mission is to figure out how far it went in that very first hour. It's like being a detective, but with kilometers instead of clues!

Setting Up the Problem

  • Total Distance: The car covers a total of 236 kilometers in three hours. That's our big picture.
  • Hour 1 vs. Hour 2: The car goes 12 kilometers further in the first hour than in the second. This means if we know the distance of the first hour, we can easily find the second hour's distance.
  • Hour 1 vs. Hour 3: In the third hour, the car travels 5 kilometers less than in the first hour. Again, knowing the first hour's distance is key.

Let's Use Algebra

To make things easier, let's use a little algebra. We'll call the distance traveled in the first hour "x".

  • Hour 1: x kilometers
  • Hour 2: x - 12 kilometers (because it's 12 km less than hour 1)
  • Hour 3: x - 5 kilometers (because it's 5 km less than hour 1)

Now, we know that the sum of these three distances equals the total distance of 236 kilometers. So we can write an equation:

x + (x - 12) + (x - 5) = 236

Solving the Equation

Now comes the fun part – solving for "x"! Let's simplify and solve this equation together. This is where the rubber meets the road, or rather, where the math meets the mileage!

  1. Combine Like Terms: First, let's gather all the 'x' terms and the constant numbers:

    3x - 17 = 236

  2. Isolate the 'x' Term: To get the 'x' by itself, we need to get rid of the -17. We do this by adding 17 to both sides of the equation:

    3x = 236 + 17 3x = 253

  3. Solve for 'x': Now, to find 'x', we divide both sides of the equation by 3:

    x = 253 / 3 x = 84.33 (approximately)

So, based on our calculations, the car traveled approximately 84.33 kilometers in the first hour. Now, remember, this is an approximate value. Depending on the context of the problem, you might need to round it to the nearest whole number or a specific decimal place. But for now, we have a pretty solid answer!

Checking Our Work

It's always a good idea to double-check our answer to make sure we didn't make any silly mistakes along the way. Let's plug our value of x (84.33 km) back into our original expressions for each hour:

  • Hour 1: 84.33 km
  • Hour 2: 84.33 - 12 = 72.33 km
  • Hour 3: 84.33 - 5 = 79.33 km

Now, let's add these distances together to see if they equal the total distance of 236 km:

  1. 33 + 72.33 + 79.33 = 235.99 km

Our sum is extremely close to 236 km. The slight difference is due to the rounding we did earlier. If we used a more precise value for 'x', we'd get even closer to 236 km. But for all practical purposes, we can be confident that our answer is correct.

Real-World Implications

This type of problem-solving isn't just for math class, guys. It's also relevant in real-world scenarios. For instance, delivery companies use similar calculations to optimize routes and estimate delivery times. They need to consider factors like distance, speed, and traffic to ensure that packages arrive on time.

Applications in Logistics

In the logistics industry, professionals often deal with complex transportation problems. They might need to determine the most efficient way to transport goods from one location to another, taking into account factors such as distance, fuel costs, and delivery deadlines. By using mathematical models and algorithms, they can find optimal solutions that minimize costs and maximize efficiency. This is especially useful for companies that have strict budgets. Logistics managers can use these mathematical approaches to ensure they stay under budget. For example, a logistics company might use a system of equations to determine the best route for a fleet of trucks, considering factors such as distance, traffic patterns, and fuel consumption. By solving these equations, they can identify the route that minimizes fuel costs and delivery times, ultimately saving the company money and improving customer satisfaction. This is a crucial role, as logistics is a cornerstone of supply chains worldwide. These methods not only optimize costs but also reduce environmental impact by minimizing fuel consumption and emissions.

Urban Planning

Urban planners also use math to design efficient transportation systems within cities. They might need to determine the optimal locations for bus stops, train stations, and bike lanes to ensure that people can easily get around. By analyzing data on population density, traffic patterns, and commuting habits, they can make informed decisions that improve the accessibility and livability of cities. Efficient transportation systems are essential for supporting economic growth, reducing traffic congestion, and improving air quality in urban areas. For example, urban planners can apply math to optimize traffic flow, design pedestrian-friendly streets, and create efficient public transportation networks. When designing public transportation, city planners can use mathematical models to determine the optimal routes for buses and trains, taking into account factors such as population density, ridership patterns, and travel times. By optimizing these routes, they can maximize the number of people who can access public transportation, while minimizing travel times and costs. They might also use mathematical models to predict how new developments will impact traffic patterns and infrastructure needs, allowing them to plan for future growth and development.

Personal Travel

Even in our personal lives, we can use these skills to plan trips, estimate travel times, and make informed decisions about transportation options. Whether we're driving, flying, or taking public transit, understanding the relationships between distance, speed, and time can help us make the most of our journeys. In our daily lives, it is helpful to estimate travel times. Also, it helps people to be on time for meetings, and avoid any late fees. This translates to a better work life, and avoiding penalties or extra charges. You can also use these skills to plan road trips, estimate travel times, and budget for expenses such as gas and tolls. By applying basic mathematical principles, you can make informed decisions that save you time and money, while ensuring a safe and enjoyable journey.

Wrapping Up

So, there you have it, guys! We successfully navigated this kilometer conundrum and found that the car traveled approximately 84.33 kilometers in the first hour. Remember, math isn't just about numbers and equations – it's about problem-solving and critical thinking. These skills can be applied to a wide range of situations in our daily lives, from planning a road trip to optimizing a delivery route. Keep practicing and exploring, and you'll be amazed at what you can achieve!