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

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Retired Moderator
Joined: 18 Jul 2008
Posts: 893
A swimmer makes a round trip up and down the river. It takes  [#permalink]

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06 Nov 2008, 16:03
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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Manager
Joined: 02 Nov 2008
Posts: 56

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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
VP
Joined: 05 Jul 2008
Posts: 1328

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06 Nov 2008, 20:03
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.
Retired Moderator
Joined: 18 Jul 2008
Posts: 893

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

OA and source posted soon
Manager
Joined: 05 Jul 2008
Posts: 131
GMAT 2: 740 Q51 V38

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07 Nov 2008, 07:31
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
VP
Joined: 30 Jun 2008
Posts: 1004

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07 Nov 2008, 07:44
1
DavidArchuleta 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

Manager
Joined: 05 Jul 2008
Posts: 131
GMAT 2: 740 Q51 V38

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07 Nov 2008, 07:49
amitdgr wrote:
DavidArchuleta 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.
Retired Moderator
Joined: 18 Jul 2008
Posts: 893

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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.
Manager
Joined: 05 Jul 2008
Posts: 131
GMAT 2: 740 Q51 V38

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07 Nov 2008, 07:58
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
Retired Moderator
Joined: 18 Jul 2008
Posts: 893

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

What happens if there is no current?
VP
Joined: 05 Jul 2008
Posts: 1328

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07 Nov 2008, 08:19
1
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.
Retired Moderator
Joined: 18 Jul 2008
Posts: 893

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07 Nov 2008, 08:37
Good explanation gang.

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

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: A Swimmer &nbs [#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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