A swimmer makes a round trip

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member; Thanked: 17 times

by rahul.s » Sat Jan 30, 2010 9:41 am

A swimmer makes a round trip up and down the river which takes her x hours. If the next day she swims the same distance with the same speed in still water, which takes her y hours, which of the following statements is true?

A) x > y
B) x < y
C) x = y
D) x = (1/2)*y
E) none of the above

OA: A

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Source: Beat The GMAT — Data Sufficiency | Sat Jan 30, 2010 9:41 am

scoobydooby: Legendary Member; Posts: 1035; Joined: Wed Aug 27, 2008 10:56 pmFollowed by: 1 member; Thanked: 104 times

by scoobydooby » Sat Jan 30, 2010 10:05 am

substituting numbers could be an option

let upstream, downstream distance be 10m, speed of the man be 5m/s, speed of stream be 1m/s
total time taken(x): upstream time+downstream time= 10/(5-1)+10/(5+1)=25/6~4.1

total time taken in still water with same distance and speed (y): 20/5=4
=> x>y
hence A

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jan 30, 2010 10:07 am

let speed of person=s and speed of water=w;distance of one side =d; time for up and down in running water=x and time in still water=y

x={d/(s-w)} +{d/(s+w)}=d[2s/(s^2-w^2)

y=2d/s(w=0)
mutliply and divide y by s

y=2ds/s^2

s^2 always >s^2-w^2

hence y will always be < x
or x>y

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Jan 30, 2010 12:41 pm

rahul.s wrote:A swimmer makes a round trip up and down the river which takes her x hours. If the next day she swims the same distance with the same speed in still water, which takes her y hours, which of the following statements is true?

A) x > y
B) x < y
C) x = y
D) x = (1/2)*y
E) none of the above

OA: A

Let 'a' be swimmers speed and b be the stream speed. Let the total distance (one way) be m

m/(a+b) + m/(a-b) = x
2ma/(a^2-b^2) = x
1/x = 1/2 (a/m - b^2/am)

2m/a = y

1/x = (1/y - b^2/am) (a, m are positive)

=> 1/x < 1/y
=> x> y

Always borrow money from a pessimist, he doesn't expect to be paid back.

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