Hi I just want to check this. It's from a recent test I took and the answer I got didn't match any of the choices. If a car travels $x$ miles at $Y$ miles per hour, and then another $x$ miles at $Z$ miles per hour, what is the average speed during the trip? It should just be the total miles divided by the total time right? That's $$\frac{2x}{\frac{x}{Y} + \frac{x}{Z}}$$
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2Yes, your answer is correct. It can be written more elegantly as $2YZ/(Y+Z)$. – M. Wind May 10 '15 at 22:36
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1Try multiplying your answer by $$\frac{\frac{1}{x}}{\frac{1}{x}}$$ – John Joy May 11 '15 at 13:54
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Be careful about average velocity and average speed. If you want to calculate average speed, then your calculation is ok. But average velocity is $ \frac{displacement}{time}$. So if the car moves x miles to the east and then x miles to the west, then the average velocity is $0$.
rackne
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John and Peter live on the equator. They decide to make a trip around the world. They travel east. After 20.000 kilometers Peter decides to stop. He returns home, travelling west. John continues to travel eastward. After exactly one year both John and Peter return home. What was the average speed of John and Peter? What was their average velocity? – M. Wind May 11 '15 at 01:15