What is the average speed for the entire duration? Trick?

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SUMMARY

The average speed of a motorcycle traveling up a hill at 10 miles per hour and down at 25 miles per hour is not calculated by simply averaging the two speeds. Instead, the correct method involves determining the total distance traveled and the total time taken. The average speed is defined as total distance divided by total time, leading to a final average speed that is lower than the naive average of 7.5 miles per hour. This discussion highlights a common misconception in calculating average speed in scenarios involving different speeds for equal distances.

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  • Knowledge of distance, speed, and time relationships
  • Ability to apply mathematical reasoning to physics problems
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  • Research the formula for average speed in varying speed scenarios
  • Study kinematic equations related to motion
  • Explore examples of average speed calculations in physics
  • Learn about common errors in speed and distance problems
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This discussion is beneficial for students studying physics, educators teaching kinematics, and anyone looking to deepen their understanding of average speed calculations in real-world scenarios.

Perseverence
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Homework Statement


A motorcycle goes up a hill at a constant speed of 10 miles per hour and comes down at the speed of 25 miles per hour what is the average speed for the entire duration?

Homework Equations


Vavg =(vf-vi)÷2

The Attempt at a Solution


It seems very straightforward that this would be 25 - 10 / 2. Making the average speed 7.5 miles per hour. But that is not the answer given in the solution. Is the solution set wrong? Thank you for your help. This is making me crazy.
 
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@Perseverence one of the most useful tricks in math is to think about things taken to their extreme. Suppose you go up a 1 mile long hill at 10,000 mph. It would take you approximately no time at all. Now you come down the hill at 1 mile per hour. It will take you an hour. Do it make any sense to you to say that the average speed would be (10000 - 1)/2 mph? That would make for a round trip of approximately zero time despite the fact that the trip down took an hour.
 
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