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#1 2016-06-19 05:21:29

Srikantan
Member
From: Tanjore
Registered: 2016-06-04
Posts: 42

Race distance

A race over a distance of 'd' m was conducted between A ,B&C in pairs. A wins over B by 30 m .
B wins over C by  20 m & A wins over C by 48 m.
Find 'd'.

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#2 2016-06-19 05:37:35

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Race distance


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#3 2016-06-19 05:38:34

Srikantan
Member
From: Tanjore
Registered: 2016-06-04
Posts: 42

Re: Race distance

Explanation please

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#4 2016-06-19 13:52:30

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Race distance

Hi;

If we call

a the speed of A

b the speed of B

c the speed of C

t1 = A's time to complete the track

t2 = B's time to complete the track.

We now have these relationships which can be derived from the problem:

Expanding line 1)

Using the substitutions from 2) and 3)

Noticing that the middle equation has d isolated we solve that.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2016-06-20 07:33:16

Srikantan
Member
From: Tanjore
Registered: 2016-06-04
Posts: 42

Re: Race distance

Awesome. Thanks

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#6 2016-06-20 08:00:00

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Race distance

For some reason it was a very difficult problem for me. After fiddling with it for more than an hour I sort of stumbled upon a correct order of substitutions. In short, looks like I got lucky.

The EM gave an answer in minutes but I did not know how to turn it into something acceptable to a student.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2016-06-20 16:41:27

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Race distance


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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