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# This is MGMAT's challenge problem of the week. Have fun !

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Joined: 07 Jul 2004
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This is MGMAT's challenge problem of the week. Have fun ! [#permalink]  09 Jan 2006, 00:48
This is MGMAT's challenge problem of the week. Have fun !

Alex and Brenda both stand at point X. Alex begins to walk away from Brenda in a straight line at a rate of 4 miles per hour. One hour later, Brenda begins to ride a bicycle in a straight line in the opposite direction at a rate of R miles per hour. If R > 8, which of the following represents the amount of time, in terms of R, that Alex will have been walking when Brenda has covered twice as much distance as Alex?
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CEO
Joined: 20 Nov 2005
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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Kudos [?]: 132 [0], given: 0

Let time "Alex will have been walking" = t

Distance covered by Alex = 4t
Distance covered by Brenda = R (t-1)

4t * 2 = R(t-1)
t = R/(R-8)
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

VP
Joined: 21 Sep 2003
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Location: USA
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Kudos [?]: 39 [0], given: 0

ps_dahiya wrote:
Let time "Alex will have been walking" = t

Distance covered by Alex = 4t
Distance covered by Brenda = R (t-1)

4t * 2 = R(t-1)
t = R/(R-8)

too fast dahiya!

x = 4t
2x = R(t-1) solving for t we get

t = R/(R-8)
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"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Director
Joined: 17 Dec 2005
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Can someone please solve the following explicitly?

4t * 2 = R(t-1)
VP
Joined: 21 Sep 2003
Posts: 1065
Location: USA
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Kudos [?]: 39 [0], given: 0

Can someone please solve the following explicitly?

4t * 2 = R(t-1)

Isn't it:

8*t = R*t - R
Since R>8,

R*t-8*t = R
t (R-8) = R
ot t = R/(R-8)
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

Senior Manager
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Let the time reqd be t ,

2(4+ 4t) = Rt
t = 8/(R-8)
Director
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Thanks giddi

Don't know why I couldn't make it too.
VP
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hkm_gmat wrote:
Let the time reqd be t ,

2(4+ 4t) = Rt
t = 8/(R-8)

hkm_gmat, didn't you calculate the time that Brenda took. They have asked for time that Alex took. So 1 needs to be added to your answer.

T(Alex) = 8/(R-8) + 1
= R/(R-8)

Is my reasoning OK?
_________________

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."

- Bernard Edmonds

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
Followers: 23

Kudos [?]: 194 [0], given: 0

I've got the same . The OE for this question is not out yet, but I'm pretty sure all of us breezed through this one.
Director
Joined: 04 Oct 2005
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Location: Chicago
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Kudos [?]: 5 [0], given: 0

I too got R/ R-8 but took almost 4 min
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