Problem 44 - Prealgebra

Question

Hybrid cars can get up to 52 miles per gallon of gas. How far can the car travel on \(\frac{3}{4}\) gallon of gas?

Step-by-Step Solution

Answer

The car can travel 39 miles.

Step 1: Understand the Problem

We need to calculate how far a hybrid car can travel with \(\frac{3}{4}\) of a gallon of gas, given that it travels 52 miles per gallon.

Step 2: Convert Problem into Mathematical Equation

The distance a car can travel is given by the formula: \( \text{Distance} = \text{Miles per Gallon} \times \text{Quantity of Gas (in gallons)} \).

Step 3: Substitute the Values

We substitute the given values into the equation: \[ \text{Distance} = 52 \times \frac{3}{4} \].

Step 4: Calculate the Distance

Calculate the distance by multiplying: \[ 52 \times \frac{3}{4} = \frac{156}{4} = 39 \]. The car can travel 39 miles on \(\frac{3}{4}\) gallon of gas.

Key Concepts

Mileage Calculation

Mileage calculation is an essential skill that helps us understand how efficiently a vehicle uses fuel. It's often measured in miles per gallon (MPG), indicating how many miles a vehicle can travel using one gallon of gas. Reliable mileage calculation is vital for budgeting fuel costs and planning trips.
To calculate mileage, you'll typically be given the MPG of a vehicle and the amount of fuel available. In our exercise, the hybrid car has an MPG of 52. We use this information to determine how far you can travel. If you're given a fraction of a gallon, as in our exercise, it factors into the calculation through multiplication.
Here's the formula we use: \( \text{Distance} = \text{Miles per Gallon} \times \text{Quantity of Gas (in gallons)} \). By plugging in the numbers, we can easily find out how many miles the car can cover with a certain amount of gas.

Fractions in Problem-Solving

Fractions are a great way to represent parts of a whole, and they often come in handy when dealing with real-world problems. In our scenario, fractions help us calculate the distance the hybrid car travels with a partial quantity of gas.
When working with fractions in calculations, such as in our problem where the hybrid car's gas quantity is \( \frac{3}{4} \) gallons, the fraction gives us the proportion of one full unit—in this case, one full gallon.
When multiplying a fraction with another number, like the car's mileage per gallon, follow these steps:

• Multiply the numerator (top of the fraction) by the number.
• Leave the denominator (bottom of the fraction) as it is and then multiply the number by this fraction.

The result gives you part of the total based on the fractional amount. This approach allows us to handle parts of gallons, making mileage calculations more precise.

Mathematical Equations

Mathematical equations act as tools that help us translate real-world scenarios into solvable problems. In our context, these equations allow us to determine potential travel distances based on given inputs.
Let's break down the equation concept used in this problem: \( \text{Distance} = \text{Miles per Gallon} \times \text{Quantity of Gas in gallons} \). This equation helps us seamlessly convert fuel consumption values into predicted travel distances, allowing for accurate planning.
Creating an equation involves identifying the relationship between different quantities involved in a problem. Once you have your equation, substitute the proper values to solve it. This will give you a reliable solution.

• Identify the known quantities (e.g., miles per gallon, gallons).
• Determine how these relate (e.g., multiplying to find distance).
• Be consistent with units to ensure accuracy.

An equation like this is versatile, meaning you can adjust the quantities to get different insights, such as how much gas is needed for a specific distance.