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A swimmer makes a round trip up and down the river. It takes

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A swimmer makes a round trip up and down the river. It takes [#permalink]

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New post 06 Nov 2008, 16:03
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A swimmer makes a round trip up and down the river. It takes him X hours. The next day he swims the same distance with the same speed in the still water. It takes him Y hours. What can we say about X and Y ?

X>Y
X<Y
X=Y
X=1/2Y
none of the above

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Re: A Swimmer [#permalink]

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New post 06 Nov 2008, 16:31
IMO X=Y

Swimmer = x
Current = c

Relative speed Downstream = x+c
upstream = x-c

Extra speed gained while downstream will cancel out speed lost going upstream , Hence it's like still water

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Re: A Swimmer [#permalink]

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New post 06 Nov 2008, 20:03
bigfernhead wrote:
A swimmer makes a round trip up and down the river. It takes him X hours. The next day he swims the same distance with the same speed in the still water. It takes him Y hours. What can we say about X and Y ?

X>Y
X<Y
X=Y
X=1/2Y
none of the above


I would say X > Y or E . But Can you tell me that he is NOT Phelps??

B T W Where is this Q. This leaves so much room for imagination.

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 07:15
How do you get X > Y?

OA and source posted soon ;-)

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 07:31
bigfernhead wrote:
A swimmer makes a round trip up and down the river. It takes him X hours. The next day he swims the same distance with the same speed in the still water. It takes him Y hours. What can we say about X and Y ?

X>Y
X<Y
X=Y
X=1/2Y
none of the above


Hi,
x: speed of the swimmer (km/h)
y: speed of the water (km/h)
So:
x-y: speed of the swimmer down the river
x+y: speed of the swimmer up the river

Because the distance doesn't have an important role in this problem so I will assume that the distance is 1km
(this swimmer is so strong)
=> Time of the trip at the first day:
1/(x-y) + 1/(x+y)= 2x/(x2-y2)

time of the trip at the second day:
2/x= 2x/x2

We can easily see that
2x/(x2-y2) > 2x/x2
=> X> Y

Hehe, my favourite AI David Archuleta' debut album is released on 11th November. You can have full legal preview at:
http://www.washfm.com/cc-common/ondemand/music.html?apid=5014 or http://www.snarkyarchies.com/2008/11/um-apparently-whole-album-is-on-z100.html

http://www.cavexupro.com/NCH/David%20Archuleta/David%20Archuleta%20-%20You%20Can%20(Full).mp3

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 07:44
1
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DavidArchuleta wrote:
bigfernhead wrote:
A swimmer makes a round trip up and down the river. It takes him X hours. The next day he swims the same distance with the same speed in the still water. It takes him Y hours. What can we say about X and Y ?

X>Y
X<Y
X=Y
X=1/2Y
none of the above


Hi,
x: speed of the swimmer (km/h)
y: speed of the water (km/h)
So:
x-y: speed of the swimmer down the river
x+y: speed of the swimmer up the river

Because the distance doesn't have an important role in this problem so I will assume that the distance is 1km
(this swimmer is so strong)
=> Time of the trip at the first day:
1/(x-y) + 1/(x+y)= 2x/(x2-y2)

time of the trip at the second day:
2/x= 2x/x2

We can easily see that
2x/(x2-y2) > 2x/x2
=> X> Y

Hehe, my favourite AI David Archuleta' debut album is released on 11th November. You can have full legal preview at:
http://www.washfm.com/cc-common/ondemand/music.html?apid=5014 or http://www.snarkyarchies.com/2008/11/um-apparently-whole-album-is-on-z100.html

http://www.cavexupro.com/NCH/David%20Archuleta/David%20Archuleta%20-%20You%20Can%20(Full).mp3


I think the portion in red should be
x+y: speed of the swimmer down the river.
x-y: speed of the swimmer up the river.

_________________

"You have to find it. No one else can find it for you." - Bjorn Borg

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 07:49
amitdgr wrote:
DavidArchuleta wrote:
bigfernhead wrote:
A swimmer makes a round trip up and down the river. It takes him X hours. The next day he swims the same distance with the same speed in the still water. It takes him Y hours. What can we say about X and Y ?

X>Y
X<Y
X=Y
X=1/2Y
none of the above


Hi,
x: speed of the swimmer (km/h)
y: speed of the water (km/h)
So:
x-y: speed of the swimmer down the river
x+y: speed of the swimmer up the river

Because the distance doesn't have an important role in this problem so I will assume that the distance is 1km
(this swimmer is so strong)
=> Time of the trip at the first day:
1/(x-y) + 1/(x+y)= 2x/(x2-y2)

time of the trip at the second day:
2/x= 2x/x2

We can easily see that
2x/(x2-y2) > 2x/x2
=> X> Y

Hehe, my favourite AI David Archuleta' debut album is released on 11th November. You can have full legal preview at:
http://www.washfm.com/cc-common/ondemand/music.html?apid=5014 or http://www.snarkyarchies.com/2008/11/um-apparently-whole-album-is-on-z100.html

http://www.cavexupro.com/NCH/David%20Archuleta/David%20Archuleta%20-%20You%20Can%20(Full).mp3


I think the portion in red should be
x+y: speed of the swimmer down the river.
x-y: speed of the swimmer up the river.



Oh, thank you!
I'm kinda in high mood tonight.
Thanks again.

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 07:52
How do you get the speed to be:

x+y: speed of the swimmer down the river.
x-y: speed of the swimmer up the river.

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 07:58
bigfernhead wrote:
How do you get the speed to be:

x+y: speed of the swimmer down the river.
x-y: speed of the swimmer up the river.

Haha, the water pushes you when you swim down the river. (coz you and the river have the same direction)
The water pulls you when you swim up the river (you and the water have counter directions).
Buy David Archuleta's debut album, everyone. It sounds so great. It helps you get 800 gmat score. haha

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 08:15
How does one assume that the water is pushing up or down?

What happens if there is no current?

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 08:19
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bigfernhead wrote:
How does one assume that the water is pushing up or down?

What happens if there is no current?


downstream means you go with the water and upstream means you against the water. As I said, an assumption has to be made that no one can go at a faster or equal speed while going upstream compared to speed of downstream and the speed of swimmer and current stayed the same through out the time.

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Re: A Swimmer [#permalink]

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New post 07 Nov 2008, 08:37
Good explanation gang.

This is from the GMAT Sets and answer is X>Y

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Re: A Swimmer   [#permalink] 07 Nov 2008, 08:37
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A swimmer makes a round trip up and down the river. It takes

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