Question

Find the average rate as indicated. \(1,100,000,000\) miles are driven to move the mail in the United States per year. Find the rate per week. Round to the nearest million miles.

Short answer

The average rate of miles driven per week to move mail in the United States is approximately 21 million miles.

Step-by-step solution

Identify Information

We are given that the total distance driven in a year for moving mail in the United States is 1,100,000,000 miles and we need to find the weekly rate of travel.

Determine Number of Weeks in a Year

There are 52 weeks in a year. This will be used as the denominator to compute the weekly rate.

Calculate Rate per Week

Divide the total distance driven, 1,100,000,000 miles, by 52 weeks. This gives us approximately 21,153,846.15 miles per week.

Round Off to the Nearest Million Miles

As per the problem's instructions, we need to round off the answer to the nearest million miles. So, rounding 21,153,846 to the nearest million gives us 21,000,000 miles per week.

Key concepts

Rate of Change

The rate of change refers to how one quantity changes in relation to another. In our context, it expresses how distance varies over time. Specifically, it measures how many miles are covered within a specific time frame, such as a week.

When trying to find the average rate of change for moving mail per week, we first gather the total distance driven annually and then divide it by the number of weeks in that year. This simplifies to a unit rate that reflects the average mileage covered in a single week. Understanding the rate of change is crucial for a variety of real-world applications, such as planning delivery routes or budgeting fuel costs.

Unit Rate

A unit rate breaks down a given amount to a 'per one' basis, providing a way to compare different quantities. In our exercise, the unit rate is the distance driven per week.

After dividing the annual mileage by the number of weeks, you get a rate that represents the consistent travel distance necessary each week to achieve the annual total. For students, recognizing the unit rate can help them grasp how large numbers apply to everyday periods like a week, which can be more meaningful and manageable.

Rounding Numbers

Rounding numbers is a mathematical technique used to simplify figures, making them easier to work with or understand. Rounding to the nearest million involves looking at the digit in the hundred thousands place and determining if the number should be adjusted up or down to the closest number with zeros trailing the millions place.

In our case, the weekly rate of mileage initially computes to 21,153,846.15. Rounding this number to the nearest million involves considering '153,846.15' and recognizing that the hundred thousand digit, 1, is less than 5, which means the original number is rounded down to 21,000,000. This makes it more approachable and practical for reporting or planning purposes.

Arithmetic Division

Arithmetic division is the process of dividing one number by another to find how many times the divisor fits into the dividend. In this example, we divide the total annual miles, 1,100,000,000, by the number of weeks in a year, 52.

The division is necessary to distribute the total into smaller, weekly portions. The result of the division must be accurate to reflect the correct weekly mileage, which will then be rounded for ease of interpretation. Students should practice this step with large numbers to ensure their calculations lead to a correct and meaningful rate of change.