1. Understanding Average Rate:
Average rate tells you how much something changes *on average* over a period of time or distance. It's the total change divided by the total time or distance. The most common example is average speed.
2. Key Formula:
The basic formula for average rate is:
Average Rate = Total amount / Total time (or distance)
3. Solving Problems: Step-by-Step
Let's look at examples to illustrate the process.
Example 1: Average Speed
* Problem: A car travels 120 miles in 3 hours. What is its average speed?
* Steps:
1. Identify the total amount: The total distance is 120 miles.
2. Identify the total time: The total time is 3 hours.
3. Apply the formula: Average speed = Total distance / Total time
4. Calculate: Average speed = 120 miles / 3 hours = 40 miles per hour
* Answer: The car's average speed is 40 miles per hour.
Example 2: Average Number per Unit of Time
* Problem: A baker makes 72 cookies in 6 hours. What is the average number of cookies he makes per hour?
* Steps:
1. Identify the total amount: The total number of cookies is 72.
2. Identify the total time: The total time is 6 hours.
3. Apply the formula: Average cookies per hour = Total cookies / Total time
4. Calculate: Average cookies per hour = 72 cookies / 6 hours = 12 cookies per hour
* Answer: The baker makes an average of 12 cookies per hour.
Example 3: Slightly More Complex
* Problem: A cyclist rides 20 miles in 2 hours, then rests for 1 hour, and then rides another 15 miles in 1.5 hours. What is the cyclist's average speed for the entire trip?
* Steps:
1. Find total distance: 20 miles + 15 miles = 35 miles
2. Find total time: 2 hours + 1 hour + 1.5 hours = 4.5 hours
3. Apply the formula: Average speed = Total distance / Total time
4. Calculate: Average speed = 35 miles / 4.5 hours ≈ 7.8 miles per hour (You might need a calculator for this step depending on your 6th-grade curriculum)
* Answer: The cyclist's average speed for the entire trip is approximately 7.8 miles per hour.
Important Note: Average rate problems often involve units. Make sure you keep track of the units and include them in your answer (miles per hour, cookies per hour, etc.). This helps you understand what the answer represents.