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Chapter 3: Problem 16

APPLICATION Nicholai's car burns \(13.5\) gallons of gasoline every 175 miles. a. What is the car's fuel consumption rate? (fi) b. At this rate, how far will the car go on 5 gallons of gas? c. How many gallons does Nicholai's car need to go 100 miles?

Short Answer

Expert verified
a) 12.96 miles/gallon, b) 64.8 miles, c) 7.72 gallons.

Step by step solution

01

Understanding the Problem

We need to find the fuel consumption rate of Nicholai's car, the distance it can travel with 5 gallons, and the gallons needed for 100 miles.
02

Finding the Fuel Consumption Rate

To find the fuel consumption rate, divide the total miles by the gallons used. This gives us:\[\text{Fuel Consumption Rate} = \frac{175 \text{ miles}}{13.5 \text{ gallons}} \approx 12.96 \text{ miles per gallon}\]
03

Calculating Distance with 5 Gallons

Use the consumption rate to find out how far the car travels on 5 gallons. Multiply the gallons by the rate:\[\text{Distance} = 5 \text{ gallons} \times 12.96 \text{ miles per gallon} \approx 64.8 \text{ miles}\]
04

Calculating Gallons Needed for 100 Miles

Use the reciprocal of the consumption rate to find gallons needed for 100 miles, which is the distance divided by the rate:\[\text{Gallons needed} = \frac{100 \text{ miles}}{12.96 \text{ miles per gallon}} \approx 7.72 \text{ gallons}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Miles per Gallon Calculation
Calculating miles per gallon (MPG) involves understanding how efficiently a vehicle uses fuel over a certain distance. This is a key measure to determine a vehicle's fuel economy. To calculate the MPG, you simply divide the number of miles driven by the number of gallons of gasoline used. For example: - Nicholai's car travels 175 miles using 13.5 gallons of gasoline. - The calculation would be: \[ \text{MPG} = \frac{175 \text{ miles}}{13.5 \text{ gallons}} \approx 12.96 \text{ miles per gallon} \] This means that for every gallon of gasoline, Nicholai's car can travel approximately 12.96 miles. A higher MPG indicates better fuel efficiency, which means more miles per gallon of fuel. Consider fuel consumption when planning trips or deciding on a vehicle as it impacts fuel costs and environmental impact.
Distance Calculation
Understanding how far a car can travel on a particular amount of fuel involves multiplying the car's miles per gallon (MPG) by the number of gallons available. This helps in determining the range of the vehicle for a given amount of fuel. For instance, to find out how far Nicholai's car can go on 5 gallons of gasoline, you compute:- Use the MPG previously calculated: \[ \text{Distance} = 5 \text{ gallons} \times 12.96 \text{ miles per gallon} \approx 64.8 \text{ miles} \]Thus, with 5 gallons of fuel, Nicholai's car can approximately cover 64.8 miles. Knowing this is helpful for planning refueling stops during long drives or estimating travel costs.
Gasoline Usage
Determining how much gasoline is needed for a certain trip is crucial for effective trip planning and budget management. It requires knowing the car's miles per gallon (MPG) and the distance you plan to travel. To find out how many gallons are required for a 100-mile trip in Nicholai's car, use the formula:- Divide the distance by the car's MPG: \[ \text{Gallons Needed} = \frac{100 \text{ miles}}{12.96 \text{ miles per gallon}} \approx 7.72 \text{ gallons} \]This means that to travel 100 miles, Nicholai's car will need approximately 7.72 gallons of gasoline. This calculation helps manage expenses and ensures sufficient fuel for the journey.

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Most popular questions from this chapter

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The local bagel store sells a baker's dozen of bagels for \(\$ 6.49\), while the grocery store down the street sells a bag of 6 bagels for \(\$ 2.50\). a. Copy and complete the tables showing the cost of bagels at the two stores. Bagel Store \begin{tabular}{|l|l|l|l|l|l|l|} \hline Bagels & 13 & 26 & 39 & 52 & 65 & 78 \\ \hline Cost & & & & & & \\ \hline \end{tabular} Grocery Store \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|} \hline Bagels & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 & 60 \\ \hline Cost & & & & & & & & & & \\ \hline \end{tabular} b. Graph the information for each market on the same coordinate axes. Put bagels on the horizontal axis and cost on the vertical axis. c. Find equations to describe the cost of bagels at each store. d. How much does one bagel cost at each store? How do these cost values relate to the equations you wrote in \(15 \mathrm{c}\) ? e. Looking at the graphs, how can you tell which store is the cheaper place to buy bagels? f. Bernie and Buffy decided to use a recursive routine to complete the tables. Bernie used this routine for the bagel store: \(6.49\) ????A Ans 2 ? ?ten Buffy says that this routine isn't correct, even though it gives the correct answer for 13 and 26 bagels. Explain to Bernie what is wrong with his recursive routine. What routine should he use?
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