# Average speed

1. May 12, 2007

### ahoy hoy

im stuck as to how to approach this in a mathematical way..
"a car travels from melbourne to moe at an average speed of 80km/h. what is least number of times the speedometer reads 80km/hr ? Explain".
thanks.

2. May 12, 2007

### mjsd

ok... sounds like a "trick" question... I guess if you wanna reach an average of 80, the speedometer must at some point get above 80, taking into account the fact that you will have to start from rest (ie. traveling at below 80 at some stage) and slow down or stop at intersection etc... so I would say at least twice assuming a smooth ride with no intermediate stoppages ...

3. May 12, 2007

### ahoy hoy

mm i get wat u mean.
i think its safe to assume that question is gaylord.
thanks heaps.

4. May 12, 2007

### Kuno

Do they give you how long it took or the distance at all?

I'm thinking it may be possible to use the mean value theorem. But then you would need a position function and the time it took to get there.

5. May 12, 2007

### ahoy hoy

nothing. i dont think they expect us to go out of our way and calculate distance between the two well known suburbs. im ok with settling with the logic of mjsd

6. May 12, 2007

It is indeed a mean value theorem problem. Let x be time, and f(x) be the distance traveled so far. Suppose that the car starts at t=a, and reaches the destination at t=b.

What is (f(b)-f(a))/(b-a)

What is f'(x)?

7. May 12, 2007

### Gib Z

In a very unrealistic way of driving your car, the least number of times should be 1 i think >.<

Maybe the 2nd time msjd was talking about is when he's arrived at the destination? The question just says traveled to that place, doesn't have to stop there.

8. May 14, 2007

### duke_nemmerle

yes the answer's definitely 1 because you could simply go 79 for most of the trip and then cross over into high speeds to reach an average of 80 in the last minute. How to tie this rigorously to the MVT(which is what others are saying and was my intuition) is not immediately clear to me, but it makes intuitive sense.

9. May 14, 2007

*sigh*

How could I possibly have made it any clearer without giving away the answer?

10. May 15, 2007

### Gib Z

Well this isn't the homework forum, not harm in doing so...

11. May 15, 2007

### D H

Staff Emeritus
Just because this thread is not in the homework forum doesn't mean its not someone's homework problem.