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

[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!

 

[phinds]

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.

 

[Zablas]

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...

 

[phinds]

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.

 

[hmmm27]

And I already know that the answer has to 13,2km/h

I'd find another source to cheat off of.

 

[DaveC426913]

Trick question?

"What was the average speed of the cyclist?"

On the final leg, is he still a cyclist?

 

[hmmm27]

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".

 

[Zablas]

I'd find another source to cheat off of.

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

 

[haruspex]

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, x_i, i=1 to 3 for the three distances and v_i for the three speeds. Then go through each fact in turn and express it as an equation.

 

[hmmm27]

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]

 

[rcgldr]

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.