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My guestimate (before reading the final result) was 25mph !
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But how do I transfer that into formulae or "show your working" as they used to say???
Assume distance = d
Assume time taken at ideal speed = t hours
1. At 30mph, time taken = t-1; distance travelled = 30t-30 = d
2. At 20mph, time taken = t+1; distance travelled = 20t+20 = d
Equating 1 and 2 gives
30t-30 = 20t +20; solving for t gives
10t = 50; t=5
So distance d = 30x5 - 30 = 120 miles
[check, same answer if you use d = 20x5 + 20 = 120 ]
So 120 miles travelled in 5 hours = 120/5 = 24 mph.
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x=distance to destination
y = desired time of arrival in hours
speed = distance divided by time
30 = x divided by ( y-1)
so 30y - 30= x
20 = x divided by ( y+1)
so 20y + 20 = x
so 30y - 30 = 20y +20
so 10y = 50
so y = 5 hours
so 30y-30 = x
so 150 -30 = x
x = 120 miles
darn! beaten to it by 1 minute!
Edited by SpamCan61 {P} on 29/09/2008 at 21:05
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You lot should be on Countdown.
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If they don't ask too much money, there could be every chance.
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If they don't ask too much money there could be every chance.
Only if I get access to Carol's wardrobe ;-x
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Cheers for that folks, I had myself got half waythrough that formula then lost my way.
Much appreciated, I can sleep tonight now!
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Alright then egg-heads, here's a real life scenario that has been doing my head in for too long.
I have two neighbours, one either side. We live along a rough farm track that is a dead end, +/- half a mile long. The houses are spaced evenly in the last half of this track, ie house number 1 is quarter of a mile from the metalled road , we're in the middle and the other neighbour is at the dead end, half a mile from tarmac.
Neighbour at the dead end has two cars, we have three and neighbour nearest the road has three (each car having its own driver) and broadly each driver makes the same number of journeys along the track to get to the road each day.
What is the fairest way of dividing the cost of repairs to the track?
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Forget the maths - 1/3 each is the only common sense approach
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What is the fairest way of dividing the cost of repairs to the track?
Assume your track is 12 units of length.
It' use is therefore split 12:9:6.
The guy with 12 units [at the dead end] uses 2 cars over it = 12 x 2 = 24 car_units.
You in the middle use 3 cars over your bit of track = 9 x 3 = 27 car_units.
The guy nearest the road uses 3 cars over his bit of track = 6 x 3 = 18 car_units.
So you split the cost in the ratio 24:27:18
In other words, if the quote is £6900, you split it
£2400 guy at furthest end.
£2700 piggy in the middle
£1800 guy nearest the road.
:-) If you don't want to be the mug or piggy in the middle, follow hxj's advice and save yourself some money!
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To enhance jbif's excellent approach further you could take the Livingstone approach and build in the various cars CO2 emissions ... ... ...
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It depends upon your definition of fair.
You could calculate, for each section of road, and each user;
L * n / N
where L is the length of that section
n is the number of cars owned by each user
and N is the total number of cars *which use that section of road*
Summing the values for each user, you would get 3 numbers, that of themselves mean nothing, but together represent the ratio of contributions.
From the info given, using the method I've described gives you
User 1 - 19%
Nsar - 34%
User 3 - 47%
For example, if I were user 1, and you presented me with jbif's calcs, I would protest that I use half the length of road, and have 3/8 of the number of uses of that stretch, so, it's unfair that I have to pay more than 1/4 of the total bill, when 3/16 more closely reflects my usage.
Edited by Number_Cruncher on 30/09/2008 at 00:48
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The guy nearest the road may suggest that he only uses 1/3rd of the length of the track and should only pay 1/3rd of the cost of the 1/3 he uses, i.e. 1/9th so extrapolating that:
guy at furthest end - 11/18th
piggy in the middle - 5/18th
guy nearest the road - 2/18th (1/9th)
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>>The guy nearest the road may suggest that he only uses 1/3rd of the length of the track
The houses aren't spaced like that.
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OK, it was the principal I was establishing, based on the spacing given by the OP the guy nearest the road may suggest that he only uses half of the length of the track and should only pay 1/3rd of the cost of the half he uses, i.e. 1/6th so extrapolating that:
guy at furthest end - 13/24th
piggy in the middle - 7/24th
guy nearest the road - 4/24th (1/6th)
Edited by cheddar on 30/09/2008 at 01:36
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Considering travel in one direction per day .........
The first neighbour has 3 cars each travelling 0.25 miles = 0.75 miles
Nsar has 3 cars each travelling 0.375 miles = 1.125 miles
The dead end neighbour has 2 cars each travelling 0.5 miles = 1.0 miles
Total distance travelled = 2.875 miles
First neighbour pays 0.75/2.875 = 26%
Nsar pays 1.125/2.875 = 39%
Dead end neighbour pays 1/2.875 = 35%
However, since all proportions are approximately a third, the easiest solution is for each person to pay a third.
Edited by L'escargot on 30/09/2008 at 05:54
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However since all proportions are approximately a third the easiest solution is for each person to pay a third.
The problem with that is that the guy at the end uses all of the lane, the guy in the middle uses 3/4 of the lane and the guy nearest the road only half the lane.
Also the number of cars is kind of irrelevant because it does not account for how much the cars are used or for trades people, visitors, deliveries etc.
My formula above accounts for the fact that:
The guy at the end should pay for all of 1/4 (of the lane) + half of 1/4 (of the lane) + 1/3 of a half (of the lane).
The guy in the middle should pay for half of 1/4 (of the lane) + 1/3 of a half (of the lane).
The guy nearest the road 1/3 of a half (of the lane).
Hence:
Guy at furthest end - 13/24th or 54%
Guy in the middle - 7/24th or 29%
Guy nearest the road - 4/24th or 17%
Edited by cheddar on 30/09/2008 at 10:38
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Try sorting our service charges for multioccupancy buildings! "I'm on the ground floor so don't use the lift, therefore I'm not paying for the maintenance of it" is a common scenario.
I also live in a shared cul de sac with unadopted road. 9 houses are responsible for one ninth of the cost of any repairs. Nice and easy that way.
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>> However since all proportions are approximately a third the easiest solution is for each person to pay a third. >> The problem with that is that the guy at the end uses all of the lane the guy in the middle uses 3/4 of the lane and the guy nearest the road only half the lane.
You'll see that I took into account what length of the lane each household uses, and how many cars travel along it.
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Perhaps a better way to consider the problem is as 3 seperate lanes. (This is just a paraphrasing of the possible split posted by Cheddar)
Part 1 - from the road to the 1st house, an even 3 way split between all users
Part 2 - from 1st house to Nsar's, an even 2 way split between Nsar and the end house
Part 3 - beyond Nsar's house, is totally the responsibility of the end house
Within fair usage limits, the drive is a facility, and splitting the costs further to accomodate whether someone has 2 or 3 cars on the day when the drive is laid isn't too helpful. If, however, Nsar began to operate haulage company with dozens of trucks from the land by his house, then that simplistic view might need to change!
It really depends upon how you, and the other users of the road/lane/drive define fair.
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Campaign to get the road adopted.
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I got it wrong. [and L'escargot too, as he had the same figures as I had, but presented in %]. Number Cruncher has the right answer.
I think an easy way to think about the problem is to start from the furthest end.
Divide the track in to three sections A:B:C costing £ X:Y:Z
Part A: Person 1 uses track A all by himself, irrespective of the number of cars he has, and so he pays £X for it.
Part B: Persons 1 and 2 use it in proportion of number of cars they own, in the case quoted by Nsar it is 2:3. So the cost £Y of track B is split 2/5 to person 1, and 3/5 to person 2 [i.e. Nsar].
Part C: Persons 1, 2, 3 again split the costs £Z in proportion to number of cars used over track C. In the case here, it is 2:3:3. So the cost £Z of track C is split 2/8 to person 1, 3/8 to person 2 [i.e.Nsar], and 3/8 to person 3.
Add the costs to work out how much each person has to pay.
cost to Person 1 = £X, + 2/5 of £Y, + 2/8 of £Z
cost to Person 2 (Nsar) = 3/5 of £Y, + 3/8 of £Z
cost to Person 3 = 3/8 of £Z
If the whole track is built to the same standard, then the costs £X, £Y, and £Z will be directly proportional to the lengths of the track A, B, and C.
The track leghth ratio in Nsar's case is A:B:C = 1:1:2, and for a uniform track,
therefore the costs are in the ratio X:Y:Z = 1:1:2
Plugging that in gives the costs split between the three people in the ratio 38:27:15 which equates in % terms to 47.50%:33.75%:18.75%
However, note that the track portions A, B and C can be designed/specified by the users to meet the needs of the traffic that is going to use it. It may be that person 1 decides he does not need to overspecify his part of the track as it will be used quite lightly.
If the track is built to to uniform standard, and then the costs are amortised to take account of the use/life of each section of track, then the results of my first attempt last night may be the true long term cost to each person. [In other words, track portion A will last a long time, track portion B a middling life, and track portion C will wear out quickest].
Edited by jbif on 30/09/2008 at 11:29
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>>Number Cruncher has the right answer.>>
jbif,
The number of cars is irrelevant, rather it is how much they are used that is relevant - though difficult, then you have to account for deliveries, trades people, vistors etc - all too complicated.
My figures (posted above) are a direct split based on usage of the sections of the lane as Number Cruncher concurs.
54% / 29% / 17%
Edited by cheddar on 30/09/2008 at 11:43
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>>The number of cars is irrelevant
It really depends upon how Nsar and Nsar's neighbours decide what is a fair method - the maths is the easy part of this problem!
I don't think we can say right or wrong. My first post gives the mathematically correct interpretation of Nsar's question as it was posed - whether that will be viewed by all parties as fair is another question.
Your post gives another possible interpretation of fair, but, we can't say whether it's right or wrong.
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The number of cars is irrelevant, rather it is how much they are used that is relevant
Usage of cars, as defined by Nsar:
" ... (each car having its own driver) and broadly each driver makes the same number of journeys along the track to get to the road each day. "
As I said, Number Cruncher is right - his "first post gives the mathematically correct interpretation".
Edited by jbif on 30/09/2008 at 11:52
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" ... (each car having its own driver) and broadly each driver makes the same number of journeys along the track to get to the road each day. ">>
My thoughts are based on having been in a vaguely similar position in that past and also being in a vaguely similar (though diferent again) position now.
Of course it is up to Nsar as to what he thinks is fair though I would say that today's number of cars/journeys may not apply tomorrow so setting a precedent now by calculating in cars/journeys could backfire if one or more parties change their usage drastically and may be interpreted as needing a new calculation every time a new resident arrives, someone takes in a lodger, gets rid of / aquires a car etc. Never mind visitors, deliveries etc.
However the lane is always going to be 1/2 mile long and have 3 house off it.
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I doubt whether the number of journeys is a critical factor in determining road life. Frost and anno domini are more likely factors - look at an abandoned WW2 airfield (plenty in East Anglia still). The runways are no longer useable, and that is not a factor of over-use.
I reckon splitting cost three ways is the fairest.
An alternative approach is to split the first .25 mile three ways, the next .125 two ways, and the last .125 one way. But to do this you will have to get out the tape measure and measure to the nearest inch. All depends on how large the bill is and how well you all get on.
83:146:270
17%:29%:54%
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You all forget of course that cost per meter to do the work, will vary by length.
For example If just the 1/3rd was repaired it may cost (for example) £10 metre. If all the road is done this cost could come down to £8 metre.
who should benefit from the savings? he who pays most?
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who should benefit from the savings? he who pays most?
Yes and he would if the whole lane is attended to so it costs £8 per meter rather than 10 or whatever and you divide the total bill by 54% / 29% / 17%.
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I take it there is nothing in title deeds etc that states who is responsible for road repairs?
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Good thought Bobby, but no, it's a bridleway so the Council only have to repair it to a condition that is safe for horses.
Thanks for all the replies so far - I'm glad it's not just me that has had trouble with this one.
Further complicated of course by the relative incomes and willingness of the three households.
(It's amazing what you'll tolerate if the alternative is thousands of pounds of cost).
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Question for the lawyers -Does the payment proportion that is agreed upon establish a precedent for future occupiers of the properties? Apportionment on the number of cars in regular use would seem to be a minefield! Future occupiers may not have cars (or even fuel!).
pmh2
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Your question is exactly why a lawyer would say a third each (and ours says a ninth each)- everyone can understand what they are signing up to and there are no clever loopholes for more lawyers to find.
Ease of drafting an agreement takes precedent over what is trying to be achieved - at some point in the future it will lead to tears and more lawyers bills.
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Your question is exactly why a lawyer would say a third each >>
If I lived at the end of the lane then I would agree to one third, and I may also be happy with that if I were in Nsar's position. Though if I lived nearest the road I would stick out for a more equitable calculation (as per above 54% / 29% / 17%), afterall the guy nearest the road never uses half of the lane.
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I would suggest that whatever way you did it - you may feel a formal agreement written for instance written into the deeds to avoid future disputes over maintenance and access (unless they're already there) you may get on as neighbours now but things can change and access and maintenance over joint access can lead to man sleepless nights.
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