How to Average Rates by Chris W The formula to average rates is:

Total Distance That means that to find the average rate, you must divide the total distance traveled by the total time elapsed when traveling that distance. Let's look at an example. James is walking to school. He starts off jogging at an average of 10 mph. Halfway to school, he sprains his ankle. His mom picks him up and drives him the rest of the way at an average speed of 40 mph. On the way home, James rides the bus at an average speed of 20 mph. What was James' average speed on his journey to school and back? Total Time If we were to just average all of the rates without using the proper formula, you would get the wrong answer. (10+40+20) 3 = 23 1 3 Let's try the problem while using the formula. Averaging rates is a tricky business. Most people think you can just take the two numbers and find the average. WRONG!!!!! First, let's draw a diagram to help us out. home home school Then, we will assume a distance to and from school so that we can calculate the time and total distance. Let's say 80 miles. (I know, it's unrealistic, but it works with the numbers we have here.) We then need to find the time elapsed during each section of his journey. home school home 80 miles 80 miles James sprains his ankle halfway between home and school. OWWW!!!!!!!!!! ankle-spraining spot 40 miles 40 miles That means that he travels 40 miles before he sprains his ankle, traveling at 10 mph. Then, his mom drives him for 40 miles, traveling at 40 mph. After school, he rides the bus at 20 mph for 80 miles. Using this information, we can then find out the total time that it took James to go to school and back. JOGGING: 40 miles at 10 mph: 4 hours DRIVING: 40 miles at 40 mph: 1 hour RIDING: 80 miles at 20 mph: 4 hours In total, it took James 9 hours to go to school and back.

His total distance was 80 miles each way, or 160 miles total. Since the formula is total distance/total time, we need to divide 160 (the total distance) by 9 (the total time. 160 9 = 160 9 160 9 1 9 - 7 0 63 - 7 7 7 9 So, our final answer is that James' average speed was 17 and 7/9 mph. Lauren hikes up a mountain at an average speed of 4 mph. On the way down, she bikes down at a speed of 12 mph. What was Lauren's average speed? Still don't get it? Let's look at an easier example. The first step would be to assume a distance. Let's say 12 miles each way. Now we will find the time elapsed during both legs of the journey. WALKING: 12 miles at 4 mph: 3 hours BIKING: 12 miles at 12 mph: 1 hour Now, we can find the answer. Total distance Total time 24 miles (12+12) 4 hours (3+1) The answer is... 6mph!!! To review: Here are the steps for averaging rates: 1. Assume a distance if necessary.

2. Draw a diagram.

3. Calculate the time elapsed during each leg of the journey.

4. Calculate the total distance.

5. Divide the total distance by the total time. Remember.... The formula for averaging rates is: total distance total time Thanks For watching!!!!!!!

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# How to average rates

This Prezi is on averaging rates.