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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
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- 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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