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

• Perseverence
In summary, the average speed for the entire duration of the motorcycle going up and down a hill is not simply the average of the speeds going up and down. Instead, it is calculated by dividing the total distance traveled by the total time elapsed, which takes into account the varying speeds during the trip. In this case, the correct average speed is 16.7 miles per hour.
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?

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.

@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.

jbriggs444

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

The average speed for the entire duration is not a trick. It is a simple calculation of dividing the total distance traveled by the total time taken.

## How is the average speed calculated?

The average speed is calculated by dividing the total distance traveled by the total time taken. This gives the overall speed for the entire duration.

## Why is the average speed important?

The average speed is an important measure because it gives an overall idea of how fast an object is moving during the entire duration. It can also be used to compare different objects or the same object at different times.

## Can the average speed be the same as the instantaneous speed?

No, the average speed and the instantaneous speed are different concepts. The average speed is the overall speed for the entire duration, while the instantaneous speed is the speed at a specific moment in time.

## What factors can affect the average speed?

The average speed can be affected by various factors such as traffic, terrain, and the acceleration or deceleration of the object. It can also be influenced by external forces like wind or friction.

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