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Word Problem

by Aman verma » Sat Sep 11, 2010 8:28 am
Q: Meg and Ryan starts running on a circular track in opposite directions. They start from point A and meet for the first , second and third time at B , C and A respectively. What is the ratio of speeds of Meg and Ryan ?

a) 3 : 1

b) 2 : 1

c) 4 : 1

d) 3 : 2

e) 5 : 3

OAb
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by raman19831 » Sat Sep 11, 2010 9:22 am
Here is how we go about this one:

Out of Meg and Ryan, one is a slow runner and other is a faster runner. Let the slow runner be Meg.

Now, Meg covers a distance of 2Ï€r in time T as he covers only one circle because the third point he reaches is A.

Ryan covers 2 circles (2Ï€r + 2Ï€r = 4Ï€r) in same time T because initially he covers distance till point B (where Meg and Ryan meet), then he crosses A again to reach point C (where again both meet) and then reached point A again. Hence, in the process he reaches point A the second time covering circle circumference 2 times.

Now, Speed of Meg = s1
Speed of Ryan = s2

s1/s2 = 2Ï€r/4Ï€r (T cancels out as time for both the runners is the same though distance varies)
=> s1/s2 = 1/2
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by 4GMAT_Mumbai » Sat Sep 11, 2010 9:25 am
Hi,

Method 1:

Their third meeting is at the starting point. This means that their first meeting was at a point 1/3rd of the track in the slower person's direction. In the same time, the faster guy has run 2/3rd of the track in the opposite direction. Hence, the ratio of their speeds is 2:1

Method 2:

During the faster guy's first lap, he meets the slower guy at B. 'During' the faster guy's second lap, he meets the slower guy at C. The third meeting happens 'at the end' of the faster guy's second lap. By the time the faster guy finishes his two laps, the slower guy has finished only 1 lap. Hence, the ratio is 2:1.

Hope this helps. Thanks.
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
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by Aman verma » Sun Sep 12, 2010 9:03 am
Hey Guys , many thanks !! I wouldn't have figured that out myself .
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by diebeatsthegmat » Sun Sep 12, 2010 9:15 am
Aman verma wrote:Q: Meg and Ryan starts running on a circular track in opposite directions. They start from point A and meet for the first , second and third time at B , C and A respectively. What is the ratio of speeds of Meg and Ryan ?

a) 3 : 1

b) 2 : 1

c) 4 : 1

d) 3 : 2

e) 5 : 3

OAb
ohh for this PS i drawned a circle and a triangle inside it, then look at itt about 30 s and think its B
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