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#1 2009-12-01 22:11:20
- waven
- Member
- Registered: 2009-10-06
- Posts: 11
Rates...
Q. Tim paddles his kayak upstream from his home to his friend's home, taking 2.5 hours for the journey. He returns that afternoon in 1.5 hours. If the river is flowing at 2.5km/h, find the distance to his friend's place
i check the answers and its 18.75km but i have no idea how to do the working it out.
thanks
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#2 2009-12-01 22:36:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rates...
Hi Waven;
His speed s is 10 km/h and the distance d to the friends house is 18.75 km
Set up these relations: Where s ithe speed and d = the total distance travelled coming and going.
2.5( s - 2.5) + 1.5( s + 2.5) = d
2.5( s - 2.5) = 1.5( s + 2.5)
solving: s = 10 km/h, d = 37.5 km
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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#3 2009-12-01 23:05:47
- phrontister
- Real Member
- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,893
Re: Rates...
Aah - I was too slow.
Same answer & method as Bobby's - except that I think:
2.5( s - 2.5) + 1.5( s + 2.5) = d
should read
2.5( s - 2.5) = 1.5( s + 2.5) = d
"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson
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#4 2009-12-01 23:19:20
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rates...
Hi phrontister;
That's essentially what my 2 equations say:
When you solve them you get s = 10 km/h and d = 37.5 km, which is the total distance he paddled. 1 / 2 of that of course is the distance to the friends house = 18.75 km.
I solved in terms of the total distance 37.5 km so mine reads:
2.5( s - 2.5) = 1.5( s + 2.5) = 2 ( distance one way ) = 37.5 km = d
I have edited the first post to make the point clearer.
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 2009-12-01 23:42:14
- waven
- Member
- Registered: 2009-10-06
- Posts: 11
Re: Rates...
how did you get 10km/h?? :S
Last edited by waven (2009-12-01 23:42:47)
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#6 2009-12-01 23:47:47
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rates...
Hi waven;
Where are you having trouble? Can you show me?
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 2009-12-01 23:54:58
- waven
- Member
- Registered: 2009-10-06
- Posts: 11
Re: Rates...
OHHHH, dw about it i just didnt read your last post properly thanks for the help!! 
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#8 2009-12-02 00:00:29
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Rates...
Hi waven;
Here is my step by step thinking:
2.5( s - 2.5) + 1.5( s + 2.5) = is the total distance d, where s is the speed.
2.5( s - 2.5) is the distance upstream
1.5( s + 2.5) is the distance downstream
They must be equal:
Solve for s:
Subtract 1.5s from both sides:
Add 6.25 to both sides:
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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