Ted's Car: Fuel Consumption & Cost Analysis

Hey guys! Let's dive into a practical math problem centered around Ted's new car and its fuel consumption. We'll be crunching some numbers to figure out how much Ted's car costs to run at different speeds. The data sheet from the manufacturer gives us the lowdown on fuel efficiency, and we'll use that to calculate costs. This is a great real-world example of how math, specifically basic arithmetic and unit conversions, plays a role in everyday life. We will also explore the implications of driving speed on fuel efficiency and overall expenses. It is going to be helpful when considering the best speed to drive to save money. So, buckle up, grab your calculators (or just use your phone!), and let's get started!

Understanding the Fuel Consumption Data

First things first, let's look at the fuel consumption data from the manufacturer's data sheet. It provides us with the fuel efficiency of the car at various speeds. Here's a table summarizing the information:

This table tells us how many liters of fuel the car consumes to travel 100 kilometers. For example, at 50 km/h, the car uses 7.5 liters of fuel for every 100 kilometers traveled. Understanding this data is key to solving the problem. We can see that fuel consumption varies depending on speed. It's also easy to see that the car is most efficient at 90 km/h. To calculate the cost, we also need to know the price of fuel, which is 80 cents per liter. Now, let's start the calculations!

Calculating Fuel Cost per Kilometer

To find out the cost of driving Ted's car, we need to calculate the cost per kilometer at each speed. We'll do this in two steps: First, we'll calculate the cost for 100 kilometers, and then we'll find the cost per kilometer.

Step 1: Cost for 100 Kilometers

We know the fuel consumption in liters per 100 kilometers and the cost per liter. We can use this to find the cost of fuel for 100 kilometers at each speed.

• At 50 km/h: The car consumes 7.5 liters/100km. The cost per liter is $0.80. So, the cost for 100 km is 7.5 liters * $0.80/liter = $6.00.
• At 90 km/h: The car consumes 6.0 liters/100km. The cost for 100 km is 6.0 liters * $0.80/liter = $4.80.
• At 110 km/h: The car consumes 6.5 liters/100km. The cost for 100 km is 6.5 liters * $0.80/liter = $5.20.

Step 2: Cost per Kilometer

Now that we know the cost for 100 kilometers, we can easily calculate the cost per kilometer by dividing the cost for 100 kilometers by 100.

• At 50 km/h: $6.00 / 100 km = $0.06/km.
• At 90 km/h: $4.80 / 100 km = $0.048/km.
• At 110 km/h: $5.20 / 100 km = $0.052/km.

So there you have it, folks! We now know how much it costs to drive Ted's car per kilometer at each of the given speeds. These calculations show that the most fuel-efficient speed is 90 km/h, resulting in the lowest cost per kilometer. Driving at 50 km/h and 110 km/h is more expensive, but it can be necessary depending on the situation, such as traffic, speed limits, or the urgency of your travel. This demonstrates a key concept – the relationship between speed, fuel consumption, and cost.

Impact of Speed on Fuel Costs

As we've seen, the speed at which you drive significantly impacts fuel costs. Let's break down the implications for Ted.

• At 50 km/h: Ted pays $0.06 per kilometer. This is the least efficient speed, costing him the most per kilometer. Perhaps driving at this speed is necessary in a city where there is a speed limit, but it isn't the most efficient way to save money on fuel.
• At 90 km/h: Ted pays $0.048 per kilometer. This is the most efficient speed according to the data sheet. It costs Ted the least amount of money per kilometer traveled.
• At 110 km/h: Ted pays $0.052 per kilometer. Driving at this speed is more expensive than driving at 90 km/h, but it is less expensive than driving at 50 km/h. This may be necessary on the highway, although driving at higher speeds comes with trade-offs.

This simple analysis shows that making smart choices about speed can lead to significant savings on fuel costs over time. If Ted frequently drives long distances, optimizing his speed to 90 km/h would save him money on fuel expenses. However, other factors, such as the time it takes to reach his destination, may also come into play. He might decide that the time saved by driving at 110 km/h outweighs the slightly increased fuel cost. This is the perfect example of how math helps make informed decisions.

Extended Analysis and Practical Applications

Let's extend this analysis and explore some practical applications of these calculations. Imagine Ted drives a certain distance every day or week. We can calculate his total fuel costs over a given period.

Daily Commute

Suppose Ted drives 50 kilometers each day for his commute. We can calculate his daily fuel costs at each speed:

• At 50 km/h: 50 km * $0.06/km = $3.00 per day
• At 90 km/h: 50 km * $0.048/km = $2.40 per day
• At 110 km/h: 50 km * $0.052/km = $2.60 per day

Weekly Costs

Over a week (assuming a 5-day work week), the costs would be:

• At 50 km/h: $3.00/day * 5 days = $15.00 per week
• At 90 km/h: $2.40/day * 5 days = $12.00 per week
• At 110 km/h: $2.60/day * 5 days = $13.00 per week

Monthly Costs

Over a month (assuming 4 weeks), the costs would be:

• At 50 km/h: $15.00/week * 4 weeks = $60.00 per month
• At 90 km/h: $12.00/week * 4 weeks = $48.00 per month
• At 110 km/h: $13.00/week * 4 weeks = $52.00 per month

These calculations clearly illustrate how changing driving habits can lead to significant savings over time. Ted could save up to $12 per month simply by driving at the most efficient speed during his commute. This simple illustration demonstrates the power of consistent and informed decisions in relation to fuel consumption.

Factors Influencing Fuel Efficiency

It is important to acknowledge that the data sheet's fuel consumption figures might not be the exact reality for various reasons. Several factors can influence the actual fuel efficiency of a car. Understanding these factors can help drivers make informed decisions to maximize fuel savings. Here are some key considerations:

• Driving Conditions: City driving, with frequent stops and starts, typically results in lower fuel efficiency compared to highway driving, where the car maintains a more consistent speed.
• Road Conditions: Driving on hilly or uneven terrain can increase fuel consumption as the engine works harder to maintain speed.
• Traffic Conditions: Stop-and-go traffic significantly reduces fuel efficiency because the car consumes fuel during acceleration and idling.
• Vehicle Maintenance: Proper maintenance, such as regular tune-ups, tire inflation, and oil changes, is crucial for optimal fuel efficiency. A poorly maintained car can consume more fuel than a well-maintained one.
• Vehicle Load: Carrying heavy loads in the car, such as passengers or cargo, increases fuel consumption because the engine needs to work harder to move the extra weight.
• Tire Pressure: Under-inflated tires increase rolling resistance, leading to higher fuel consumption. Maintaining the correct tire pressure is important.
• Wind and Weather Conditions: Strong headwinds or adverse weather conditions like rain or snow can also affect fuel efficiency.

Conclusion: Making Informed Choices

So, what have we learned, guys? We've explored how to calculate fuel costs based on a car's fuel consumption data, and we've discovered the impact of driving speed on those costs. The key takeaway is that understanding your car's fuel efficiency and making informed driving choices can save you money. In the case of Ted's car, driving at 90 km/h is the most economical, according to the manufacturer's data. Remember that other factors, like traffic and road conditions, can influence real-world fuel consumption.

By being mindful of your driving habits and making smart choices, you can improve fuel efficiency and save money in the long run. So, next time you're behind the wheel, consider these calculations and make the most fuel-efficient choice for your trip. And, hey, this is a great example of how simple math can make a difference in your everyday life. Keep those math skills sharp, and always look for opportunities to apply them. It's not just about the numbers; it's about making informed decisions. Drive safe, drive smart, and save some cash! I hope you enjoyed this fuel consumption analysis. Have a great day!