Problem 57 - Prealgebra

Question

If a car travels 336 miles on 15 gallons of gas, how far will the car travel on 1 gallon of gas?

Step-by-Step Solution

Answer

The car will travel 22.4 miles on 1 gallon of gas.

Step 1: Understand the Problem

The problem is asking us to find the distance the car can travel using one gallon of gas given that it can travel 336 miles on 15 gallons.

Step 2: Recognize the Relationship

Knowing the car uses 15 gallons to travel 336 miles, we need to determine how many miles it can travel per gallon. This involves finding the unit rate of miles per gallon.

Step 3: Set Up the Division

To find the miles per gallon, divide the total miles by the number of gallons. This calculation will give us the distance the car travels per gallon.

Step 4: Perform the Calculation

Use the division formula \frac{336 \text{ miles}}{15 \text{ gallons}} to get the miles per gallon calculation: \[336 \div 15 = 22.4 \text{ miles per gallon}\]

Step 5: Verify the Calculation

Double-check the math to ensure the division is correct. 336 divided by 15 equals 22.4, so the computation is accurate.

Key Concepts

Understanding Miles Per Gallon

Miles per gallon (MPG) is a measure of how far a vehicle can travel on a single gallon of fuel. It is an important concept for evaluating fuel efficiency.
MPG is universally used in many regions to compare vehicles based on fuel performance. The higher the miles per gallon, the more efficient the vehicle is because it can travel further on less fuel.
For example, knowing that a car travels 22.4 miles on just one gallon of gas can help in managing fuel costs and understanding a vehicle's performance.
It tells drivers how often they will need to refuel, thus assisting in planning longer journeys effectively. Using miles per gallon, consumers can make informed decisions regarding vehicle purchases by comparing the fuel efficiency of different models. Understanding this unit rate is crucial, especially with rising fuel prices.

Calculating Unit Rate through Division

Division for unit rate calculation is a common method in mathematics used to simplify a ratio or compare quantities. To find a unit rate:

• Identify the two quantities involved, such as miles and gallons in our scenario.
• Set up the division: Divide the total number of miles by the total number of gallons (or other relevant measures).

This calculation will yield the unit rate, miles per gallon in this context.
For instance, dividing 336 miles by 15 gallons gives us the unit rate or miles per gallon: \(336 \div 15 = 22.4\).Understanding how to perform this calculation is vital, as it provides a clear picture of fuel efficiency. Unit rate calculations help to streamline complex information into digestible, practical numbers.
By mastering division for unit rate, problem-solving in real-world scenarios becomes clearer and more efficient.

Effective Problem-Solving Steps in Math

Problem-solving in math involves a structured, logical approach to managing and solving questions. Here’s a simplified guide to effective math problem-solving:

• Understand the Problem: Carefully read the problem statement to identify the question and known data.
• Determine the Relationship: Recognize what relationships are present, like ratios or equations, and what calculations will provide the solution.
• Set Up Equations or Division: By organizing known quantities into a mathematical operation (such as division), the path to finding the solution becomes clearer.
• Calculate: Execute the arithmetic or algebraic operations to solve for the unknown.
• Verify: Double-check your calculation to ensure accuracy. Re-evaluate if the solution makes logical sense in context to the problem.

Applying these systematic steps ensures that problems are solved efficiently and correctly. Practice and familiarity with these steps enhance mathematical proficiency and confidence in problem-solving.