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

[Perseverence]

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.

 

[jbriggs444]

A good definition for average speed is total distance traveled divided by total time elapsed. Both the trip up and the trip back cover a positive distance. That is not the only problem with the solution you arrived at.

See https://www.physicsforums.com/insights/frequently-made-errors-mechanics-kinematics/

 

[phinds]

@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.