Problem 10 - Prealgebra

Question

Express each of the following rates as a ratio with the given units. Miles/Gallon On a 384 -mile trip, an economy car uses 8 gallons of gas. Give this as a rate in miles per gallon.

Step-by-Step Solution

Answer

The car's fuel efficiency is 48 miles per gallon.

Step 1: Identify the given quantities

First, we need to identify the quantities mentioned in the problem statement: the car travels 384 miles and uses 8 gallons of gas for this trip.

Step 2: Set up the ratio

To find the rate in miles per gallon, we set up the ratio of miles traveled to gallons used. The formula for this is: \[\text{Miles per Gallon} = \frac{\text{Total Miles}}{\text{Total Gallons}}\] Substituting the given values, we get:\[\frac{384 \text{ miles}}{8 \text{ gallons}}\]

Step 3: Simplify the ratio

To simplify the ratio, divide the numerator (miles) by the denominator (gallons):\[\frac{384}{8} = 48\]Therefore, the car's fuel efficiency is 48 miles per gallon.

Key Concepts

Understanding Miles per Gallon

Miles per gallon (MPG) is a measurement of how far a vehicle can travel using one gallon of fuel. It helps us understand a car's fuel efficiency. When we say a car gets 48 MPG, it means the car can travel 48 miles with just one gallon of fuel.
This is an important metric for determining how economical a car is over long distances.
By knowing the MPG, you can estimate how much you'll spend on fuel during a journey, helping in budgeting and choosing the right car for your needs.

Fuel Efficiency Calculations

Fuel efficiency calculations rely on understanding the relationship between miles driven and gallons of fuel used. The formula you use is:

• Find out how many miles you have traveled.
• Count the number of gallons you've used during the trip.
• Divide the miles by gallons to get the MPG: \(\text{MPG} = \frac{\text{Total Miles Driven}}{\text{Total Gallons Used}} \)

This calculation is straightforward. It's especially useful for comparing different vehicles or planning longer trips.
An efficient car is one that travels more miles on less fuel, reducing costs and environmental impact.

Simplifying Ratios in Real Life

Simplifying ratios is an essential math skill used in many real-world scenarios. When you simplify a ratio, you make it easier to understand and compare. To do this, divide both the numerator and the denominator by their greatest common factor (GCF).
For the exercise,

• The GCF of 384 and 8 is 8.
• By dividing both by 8, you simplify: \(\frac{384}{8} = 48 \)

This tells us that for each gallon of gas, 48 miles can be driven.
Simplifying ratios helps clarify how different quantities relate to each other, which is handy in everyday tasks like cooking or spending money effectively.