Calculating Car Speed: Melbourne to Moe

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Discussion Overview

The discussion revolves around a mathematical problem involving the calculation of a car's speed while traveling from Melbourne to Moe, specifically focusing on the average speed of 80 km/h and the least number of times the speedometer would read this speed. The scope includes mathematical reasoning and conceptual clarification.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses uncertainty about how to approach the problem mathematically.
  • Another suggests that achieving an average speed of 80 km/h would require the speedometer to exceed 80 km/h at some point, proposing at least two instances of reading 80 km/h under ideal conditions.
  • A different participant questions the clarity of the problem and suggests it may be a trick question.
  • One participant proposes using the mean value theorem, noting the need for a position function and the time taken for the journey.
  • Another participant agrees with the mean value theorem approach but expresses uncertainty about how to rigorously connect it to the problem.
  • Some participants speculate that it may be possible to achieve the average speed with only one instance of the speedometer reading 80 km/h, suggesting a strategy of driving below 80 km/h for most of the trip and exceeding it briefly at the end.
  • There is a mention of the potential for the problem to be a homework question, leading to a discussion about the appropriateness of sharing solutions.

Areas of Agreement / Disagreement

Participants express differing views on the minimum number of times the speedometer must read 80 km/h, with some suggesting it could be as few as one and others proposing at least two. The discussion remains unresolved regarding the definitive approach to the problem.

Contextual Notes

Participants note the lack of specific information about the distance or time taken for the journey, which may affect the application of the mean value theorem and the overall reasoning.

ahoy hoy
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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.
 
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ok... sounds like a "trick" question... I guess if you want to 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 ...
 
mm i get wat u mean.
i think its safe to assume that question is gaylord.
thanks heaps.
 
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.
 
nothing. i don't think they expect us to go out of our way and calculate distance between the two well known suburbs. I am ok with settling with the logic of mjsd
 
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)?
 
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.
 
Gib Z said:
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.


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.
 
*sigh*

How could I possibly have made it any clearer without giving away the answer?
 
  • #10
Well this isn't the homework forum, not harm in doing so...
 
  • #11
Just because this thread is not in the homework forum doesn't mean its not someone's homework problem.
 

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