# What is the Average Speed of the Cyclist on a Multi-Stage Journey?

• Zablas
In summary: There would also be another equation for the sum of the 3 portions of the trip. In summary, the problem presents a cyclist who travels at two different speeds for half of the trip each, before finishing the journey on foot at a slower speed. The question asks for the average speed of the cyclist, which is found to be 13.2km/h. Various attempts at solving the problem, such as using the harmonic average and creating equations for each leg of the trip, have been unsuccessful. However, the correct answer is given in the book, and the problem may require careful interpretation to reach the correct solution.
Zablas

## Homework Statement

So I have this homework exercise which I just can't seem to solve. It sound like this: "Half his time the cyclist was driving at the speed of 20km/h, half of the LEFTOVER way he drove at the speed of 16km/h. When his bike broke he finished his journey on foot at the speed of 4km/h. What was the average speed of the cyclist?" And I already know that the answer has to 13,2km/h but I just have 0 idea how to get this. Could someone show me how to do this? Thank You in advance!

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I realize you're not asking for the answer (which you already have anyway) but you have to show some effort. We don't spoon feed answers to people who show no work of their own.

Ok so I'll tell you what I've tried. I tried calculating the answer using the harmonic average. I got the answer of 8,3km/h. The I tried doing it this way:

1/v = (1/2v1) + (1/4v2) + (1/4v3)

Which gave me the answer of 9,7km/h. I'm pretty lost here...

Considering that you are not sure what you are doing, I think the way you are going about it is not helpful.

Write equations for each leg of the trip and add them up.

Zablas said:

I'd find another source to cheat off of.

Trick question?

"What was the average speed of the cyclist?"

On the final leg, is he still a cyclist?

billy_joule
DaveC426913 said:
On the final leg, is he still a cyclist?
If you're walking a bicycle, you're either a cyclist or can't afford crutches for your broken leg.

But, is he a cyclist at all ? According to the problem, he's "driving".

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hmmm27 said:
I'd find another source to cheat off of.

Well the answer is given in the same book as this exercise...

No, it's not a trick question, but it is a little tricky.
As phinds wrote, you have to convert each piece of information to an equation. Start by creating variables to go in those equations.
I suggest T for total time, xi, i=1 to 3 for the three distances and vi for the three speeds. Then go through each fact in turn and express it as an equation.

Zablas said:
Well the answer is given in the same book as this exercise...
I didn't mean to imply that you were technically cheating.

[edit: the answer given by the book is correct, despite what I said earler; I didn't read the question correctly the first time]

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haruspex said:
three distances and ... three speeds.
and also the three times. So as suggested, x1, x2, x3, for distances, v1, v2, v3, for velocities, t1, t2, t3 for times. One relevant equation would be x = v t used for each of the 3 portions of the trip.

## 1. What is the definition of average speed of a cyclist?

The average speed of a cyclist is the total distance traveled divided by the total time taken to travel that distance. It is typically measured in miles per hour (mph) or kilometers per hour (km/h).

## 2. How is the average speed of a cyclist calculated?

To calculate the average speed of a cyclist, you divide the total distance traveled by the total time taken to travel that distance. For example, if a cyclist travels 20 miles in 1 hour, their average speed would be 20 mph.

## 3. Does the average speed of a cyclist vary during a ride?

Yes, the average speed of a cyclist can vary during a ride due to factors such as terrain, weather conditions, and fatigue. It is common for a cyclist to have a higher average speed on flat terrain compared to hilly terrain.

## 4. Can the average speed of a cyclist be improved?

Yes, the average speed of a cyclist can be improved through consistent training, proper nutrition, and using efficient cycling techniques. Other factors that can help improve average speed include having a well-maintained bike and using appropriate gear.

## 5. Is average speed the only factor that determines cycling performance?

No, the average speed of a cyclist is not the only factor that determines cycling performance. Other important factors include power output, cadence, and endurance. Additionally, factors like wind speed, temperature, and road conditions can also affect cycling performance.

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