Question

A car uses fuel at a rate of 15 miles per gallon. Estimate how many miles the car can travel on 20 gallons of fuel.

Short answer

The car can travel an estimated 300 miles on 20 gallons of fuel.

Step-by-step solution

Understand what the rate is telling us

A rate of fuel consumption of 15 miles per gallon translates into the car being able to travel 15 miles on a single gallon of fuel.

Multiply the rate by the number of gallons

We need to multiply our rate of 15 miles per gallon by the total amount of fuel we have, which is 20 gallons. Doing this will give us the total miles the car can travel. This is calculated as \(15 \, miles/gallon \times 20 \, gallons = 300 \, miles\). The gallons cancel out and we are left with the miles.

Final answer

So, the car can travel an estimated 300 miles on 20 gallons of fuel.

Key concepts

Miles per Gallon

Miles per gallon (mpg) is a measure that indicates how far a car can travel using a single gallon of fuel. It is a standard unit used especially in the United States to express the fuel efficiency of vehicles. A higher mpg rating means the vehicle is more fuel-efficient, as it can travel further distance with less fuel.

Mpg is calculated by dividing the number of miles traveled by the gallons of fuel used. For example, a car with a fuel efficiency of 20 mpg would require 5 gallons of fuel to travel 100 miles. Understanding this measure is crucial for estimating travel costs, determining your vehicle's impact on the environment, and making informed decisions when purchasing a car.

Unit Rate

A unit rate is a type of ratio that expresses the quantity of one thing in comparison to a single unit of another thing. When we say a car's fuel efficiency is 15 miles per gallon, we are really referring to a unit rate. This unit rate informs us that for every one gallon of fuel consumed, the car can travel 15 miles.

The concept of the unit rate is not only applied in measuring fuel efficiency but also in various other contexts such as speed (miles per hour), packaging (cost per item), and density (population per square mile). It's a fundamental concept in understanding how different rates can be compared and applied practically. For example, knowing the unit rate of fuel consumption is essential for budgeting for a road trip or determining how often you'll need to refuel.

Multiplying Rates

When we multiply a rate by a quantity, we extend the rate to find a total. For example, if a car uses fuel at the rate of 15 miles per gallon, multiplying this rate by 20 gallons tells us how many miles the car can travel on those 20 gallons of fuel. This operation is quite common and applies rates to real-life scenarios.

To multiply rates, ensure the quantities you are working with are compatible (e.g., gallons with gallons). In our vehicle example, the equation is as follows:\[15 \, \frac{miles}{gallon} \times 20 \, gallons = 300 \, miles\]
The gallons unit cancels out and we are left with the total distance the car can travel, in miles. This method of multiplying rates can be used in many situations where you have a standard rate and need to determine an extended or total measure—like converting hourly wages to total earnings for a work period or converting unit prices to total costs of multiple items.