# A maths question I can't really explain

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#1
Hi,

This is probably more simple that I'm making it out to be but I was wondering how you'd work out a solution for the following problem.

If it consistently takes someone 60 mins to get to work by walking, and if he takes a car he can either end up at work in 5 minutes or the worst case 80 minutes (note that he can't get there any more or less than 5 or 80 minutes - these are fixed values, so he either gets there in 5 or 80 if he goes by car), what ratio of him experiencing the best case situation by car and the worst case situation by car would offset the situation where he just walks?

How would you work this out? What sort of maths would you use?

Note: this isn't really an exam question, I just made it up, I had a question similar to this but I don't remember how it was phrased just the problem.

Thanks,
Ray
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3 years ago
#2
(Original post by Rayaxer)
Hi,

This is probably more simple that I'm making it out to be but I was wondering how you'd work out a solution for the following problem.

If it consistently takes someone 60 mins to get to work by walking, and if he takes a car he can either end up at work in 5 minutes or the worst case 80 minutes (note that he can't get there any more or less than 5 or 80 minutes - these are fixed values, so he either gets there in 5 or 80 if he goes by car), what ratio of him experiencing the best case situation by car and the worst case situation by car would offset the situation where he just walks?

How would you work this out? What sort of maths would you use?

Note: this isn't really an exam question, I just made it up, I had a question similar to this but I don't remember how it was phrased just the problem.

Thanks,
Ray
If we use the expected duration of the journey as the measure, we're looking for the probabilty of the car journey being worst case, such that the expected journey by car takes longer than the expected journey by walking.

Expected length of journey by walking is 60

If we let p be the probability of worst case for the car, then:
Expected length of journey by car is 80p + 5 (1-p)

And we want p such that, 60 = 80p + 8(1-p) for the critical value of p where the expected journey is the same whether we take the car or walk.

Then convert this into a ratio.
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